i 


\r 


D    BY    M.     GIBSON. 


WHICH- 15  ANNKXKD  AN  APPENDIX,  CONTAINING 

.oKAXlON  Ox^'  SURFACES,  TABLES  OF  FOREIGN  MONEY, 
AND  BOOK-KEEMNG. 


I 


SXI:i£tJt]OT^Sri»B    EX>ITI01Sr. 


rJCnMONl): 

WEST  &  JOHNSTON,  145  MAIN  STREET. 
18G4. 


iiJ 


\. 


THE 

WILLIAM  R.  PERKINS 
LIBRARY 

OF 
DUKE  UNIVERSITY 


Rare  Books 


A 


A 


THE  ^-— « 

\ 

SOUTHEllN  SCHOOL  ARITHMETIC; 

YOUTH'S  ASSISTANT. 

CONTAINING 

THE  MOST   CONCISE  AND  ACCURATE   RULES  FOR 
PERFORMING  OPERATIONS  IN 

A.R  I  T  H  M  E  T  I  C, 

ADAPTED  TO  THE  EASY  AND  REGULAR  INSTRUCTION  OF  YOUTH, 

FOR  THE  USE  OF  SCHOOLS,  Sec. 
By  a.  &  J.  FOWLEK, 

TEACHERS    OP  AIIITHMETIO. 

REVISED     BY     M.     GIBSON, 

TO  uuicH  lo  A^^'^;xKD  an  appendix,  confaining 

MEWSUKA'LION  On'  SURFACES,  TABLES  OF  FOREIGN  MONEY, 
AND  BOOK-KEEMNG. 


E5X£l£tJBOT"YI»B    EX>ITI03Sr- 


PJCHMONl): 

WEST  &  JOHNSTON,  145  MAIN  STREET. 
1864. 


wmmamad 


E.niKRKD  Hccordinp  lo  act  of  Congress,  in  the  ycm 
hy  AitiJAH  h  .luBlAil   FoWLKK,  in  tlie  Clerk's  C>iricc  for  llic 
Kubtcra  Ditflritt  of  Tcnuet^soi-,  ui  KuoxvilK;. 


J\K  KSTKniD  acrordiiig  lo  act  oC  Coniirosi^,  in  the  year  ]Sr;'>, 
by  L.  GiKKoRD,  in  the  Clerk's  OHict?  '"ur  tho  E:is!riii  Di.sirii't 
of  Tennessee,  of  Knoxville 


Ke-extbred  according  to  act  of  Congress,  in  tlic  year  ISlV}, 
1»y  Wk»T  ik.  .TojiMSTON.  in   the  Cleik's  OlHcc,  for  llie  KasJera 

l>i-.iii,'   (.(    Vrr"iiii;i    ;it    Uii'lnimiiil. 


KECOMMENDATIONS. 


MESSRS.  FOWLERS'  ARITHMETIC. 

This  work,  which  was  handed  me  some  time  since,  for  ex- 
amination, exhibits  a  degree  of  industry  and  ability  highly 
creditable  to  the  authors.  The  order  of  arrang^ement  appears 
to  be  judicious,  and  the  iHustrations  clear  and  plain.  The  cir- 
cumstance that  it  is  primarily  adapted  to  our  national  currency, 
is,  to  me,  one  of  its  chief  recommendations;  and  were  no 
works  of  an  opposite  character  introduced  into  our  common 
schools,  we  should  soon  have  a  currency  or  mode  of  reckoning, 
simple,  uniform,  and  intelligible  to  every  one.  I  trust  the  gen- 
tlemen will  meet  with  such  encouragement  from  the  public, 
as  will  more  than  compensate  for  the  trouble  and  expense  of 
publication.  Joseph  Estabrook, 

President  of  the  East  Tennessee  College. 

Knoxville,  April  29th,  1834. 


MESSRS.  FOWLERS'  ARITHMETIC. 

From  a  hasty  examination  of  this  work,  I  would  say,  its  judi- 
cious arrangement,  the  perspicuity  and  conciseness  of  its  rules, 
the  clearness  and  simplicity  of  its  illustrations,  and  its  adaptation 
to  our  national  currency,  render  it  a  desirable  companion  for  the 
beginning  in  this  important  branch  of  education.  I  trust  the 
industry  and  ability  exhibited  by  its  youthful  authors,  will  meet 
with  liberal  encouragement. 

Allen  II.  Mathes, 
Late  Principal  of  the  Male  Acadeiny. 

Madisonville,  June  14th,  1834. 


THE  FEDERAL  INSTRUCTOR ;  OR.  YOUTHS'  ASSISTANT. 

The  above  work,  in  my  opinion,  has  considerable  merit  The 
rules  appear  to  me,  to  be  made  plain  to  tlie  understanding  of 
beginners,  and  unadvanccd  learners,  in  the  very  useful  branch 
of  knowledge  on  which  it  treats.  Hope  is  entertained  that 
Messrs.  Fowlers',  the  authors  of  it,  will  be  liberally  rewarded 
for  their  undertaking,  by  the  patronage  of  a  gencrotis  public. 

Henry  C.  Saffkll, 
Principal  of  the  Holston  Seminary. 
New-Market,  June  26th,  1835. 


ip.-^-  -.  .  ■  ']■'''■■  I  1 1      I 

iv  RECOMMENDATIONS. 

Having-  carefuHy  examined  "  Fowlers'  Arithmetic,"  I  make 
no  hesitation  in  saying  that  I  fully  concur  with  the  foregoing 
gentlemen  in  opinion,  with  respect  to  the  merits  of  the  work, 
and  cordially  unite  with  them  in  recommending  its  introduction 
into  our  schools  and  academies,  as  well  as  particularly  into  the 
Tyro's  Library. 

JosiAH  P.  SniTHf  Philom. 
Kingston,  Oct,  1836. 

_____  j 

Messrs.  Fowlers  : 

1  have  carefully  examined  your  Arithmetic,  and  must  say, 
after  twenty-five  years  experience  as  a  teacher,  that  I  have  not 
seen  a  work  of  the  kind  that  I  would  prefer  before  it,  especially 
for  young  beginners.  The  shortness,  simplicity,  and  plainness 
of  the  rules,  as  you  have  very  justly  remarked  in  your  preface, 
must  I  think  greatly  accelerate  the  progress  of*^  learners.  I 
trust  you  will  meet  with  the  patronage  of  our  fellow-citizens 
generally. 

Landon  Duncj^n. 

Giles  County,  Virginia,  March  15th,  1836. 


Messrs.  Fowlers  :  "  ?^ 

Gentlemen — I  have  carefully  examined  your  treatise  on 
Arithmetic,  and  I  think  it  superior  to  any  other  now  in  use  to 
facilitate  the  progress  of  the  young  learner,  and  is  fully  ade- 
quate for  all  the  common  business  of  our  country.  It  well 
merits  a  place  in  our  schools  and  Academies,  as  well  as  in  our 
houses.  * 

Michael  Morris, 
Teacher  of  the  EstillviUe  Academy,. 
Estillville,  Va.,  13th  July,  1836. 


. 


EXPLANATION  OF  CHARACTEKS,  SIGNS  AND 
SIGNIFICATIONS. 

=   Equal,  as  100  cts.  =  $1. 

+   More,  as  4  +  2  =  6. 

—  Less,  as  6  —  2  =  4. 

X    Into,  with,  or  multiplied  by,  as  4  X  2  =  8. 

rr  By,  i.  c.  di\'ided  by,  as  6  ~  2  =  8.  or  2)6(3. 

: : :  Proportion,  as  2  ;  4  : :  6 :  12. 

i/   Squai'c  Root,  a,s  V  64  :=  8. 

^   Cube  Root,  as  ^  64  =  4. 

y  Fourtli  Root,  as  V  16  =  2,  &c. 


JL 


(V) 


^ 


P  11 1^:  FACE. 


The  design  of  the  authors  in  brinpfinfr  this  work  before  the 
public  is,  to  teach  the  science  <»f  .Auithmetic  in  a  different  and  ; 
!  easier  manner  than  has  been  customary.  To  attain  this  object, 
J  wo  have  simplified  the  necessary  rule's,  thus  leading  the  student 
:out  of  the  darkness  uf  ignorance  by  a  plain  path,  into  the  light 
iof  knowledge.  Tl»e  shortness,  simplicity  and  plainness  of  the 
I  rules,  will  enable  the  student  to  advance  with  greater  ease  and 
I  speed  than  those  hitherto  promulged. 

As  calculating  in  English  money  is  measurably  obsolete,  the 
authors  have, with  but  iew  exceptions,  employed,  in  this  work, 
the  legal  currency  of  our  country.  Dollars  and  Cents,  Two 
things  among  us  have  been  but  too  well  fitted  to  retard  the 
progress  of  Arithmetical  knowledge;  calculations  in  pounds, 
shillings,  pence  and  far  tilings,  a  currency  unknown  among  us, 
and  unsuited  to  the  transactions  of  our  common  country  con- 
cerns; and  long,  complex  rules,  difficult  to  be  remembered, 
and  still  more  diflicult  to  comprehend.  But,  make  your  rules 
short,  familiar,  and  easy  to  be  understood,  and  the  student  is 
encouraged  to  pursue  tiie  shining  path  of  science,  thus  plainly 
pointed  out  to  him  with  alacrity  and  delight. 

Tiiough  this  work  may  appear  short,  yet  there  are  in  it  1300 
questions,  or  upwards — a  sufficiency,  we  should  think,  in  point 
of  number;  selected  so  as  to  be  useful,  and  adapted  to  the  cii-| 
cumstances  of  our  country.  ! 

Many  persons  wlio  have  ciphered  for  months,  and  some  who' 
have  gone  through  the  Arithmetic,  are  at  a  loss  because  tiiey  ■ 
do  not  understand,  or  have  not  paid  attention  to  the  rules,  i 
This  evil  will  be  the  more  easily  remedied  on  our  system,  as ; 
our  rules  are  plain  and  short,  and  may,  with  but  little  labour,  bel 
committed  to  memory.  j 

When  our  Saviour  came  into  the  v.orld,  he  was  condemned,' 
by  the  Jews  by  asking  a  simple  question — ocm  any  thing  goodl 
come  out.  of  ISazareth  ?    If  any  are  disposed,  in  a  similar  way, ; 
to  denounce  our  work,  we  would  beg  of  them  to  examine  care-j 
fully  and  candidly  before  they  decide,  and  to  remember,  that,  I 
as  the  Messiah  did  come  out  of  N*^zareth,  so,  it  is  possible  for 
a  good  Arithmetic  to  be  made  in  Tennessee.     We  are,  indeed, 
devotedly  attached  to  this  study,  and   as  we    think  we   have 
made  improvements  in  the  mode  of  teaching  it,  we  have  risked 
our  all  to  give  publicity  to  the  book,  to  enable  others  to  judge  of 
it  ^nd  to  profit  by  it. 


(vi) 


r' 


CONTENTS. 


P.IOK. 

Numeration 9 

Addition 10 

Multiplication 12 

Subtraction 16 

Short  Division 18 

Long  Division 20 

Tables  of  Money,  Weights  and  Measures 23 

Compound  Addition 25 

Compound  Multiplication , 32 

Compound  Subtraction ^ 38 

Compound  Division 43 

Reduction  Descending iCi 

Reduction  Ascending 49 

Rule  of  Two 5^ 

Rule  of  Three     56 

Double  Rule  of  Three " 61 

Practice 64 

Interest 68 

Brokerage 77 

Discount 78 

Tare  ^md  Tret 80 

Equation ,> 83 

Barter 85 

Loss  and  Gain 87 

Partnership 89 

Exchange 91 

Vulgar  Fractions ' 97 

Decimal  Fractions 107 

Involutions  or  Raising  of  Powers 113 

Square  Root ^ .  .  , 114 

Cube  Root , 117 

Single  Position 118 

Double  Position 120 

AUegaticn s 121 

ArithmetiEal  Bx)gression 122 


(7) 


■ttfSSVMasszaeBai 


8  CONTENTS. 

Tage. 

Geometrical  Progression 125 

Compound  Interest  by  Decimals 127 

Permutation 131 

Combination •  •  •  v 131 

Duodecimals .^ 132 

Promiscuous  Eiamples 134 

Appendix 141 

Mensui-ation  of  Surfaces 141 

Parallelogi'am,  &c 141 

Triangle 142 

Circle .142 

Elipsis , 143 

Mensm-ation  of  Solids 144 

Hewn  Timber,  Box,  &c 144 

To  G-auge  a  Com  House  or  Box 144 

To  make  a  Box  of  a  given  length  or  width  to  contain 

a  given  nun^ber  of  bushels,  &c 145 

The  Cylinder 146 

A  Vessel  in  the  shape  of  a  Frustrum  of  a  Cone 147 

Gauging  of  Casks 147 

Tonnage  of  Flat  Boats 148 

Tables  of  Foreign  Money 150 

A  Short  Method  of  Counting  Interest 166 

lleduction  of  Coins 166 

A  Table  of  Interest 171 

Book-Keeping 172 

Form  of  Notes,  Receipts,  &c 181 


AEITHMETIC. 


Arithmetic  is  that  part  of  the  Mathematics  which 

teaches  the  art  of  computation  by  numbers.     All  operations 

in  Arithmetic  are  performed  by  means  of  the  following 

figures,  viz:   One  1,  two  2,  three  3,  four  4,  five  5,  six  6; 

I  seven  7,  eight  8,  nine  9,  cipher  0. 


NUMERATION. 

Numeration  teaches  the  different  value  of  figures  by 
their  different  places,  and  to  express  any  proposed  numbers 
cither  by  words  or  charactei's ;  or  to  read  and  write  any  sum 
or  number. 


NUMERATION  TABLE. 


PL, 

t-i 

P-. 
o 

o 


1-5 


P    O 


ts' 


0 
0 

P-. 

CD 


o 

a. 


I 


o 


One. 

Twenty-one. 

Three  hundred  21. 

Four  thousand  321. 

54  thousand  321. 

654  thousand  321. 

7  million  054  thousand  321. 

87  million  654  thousand  321. 

987  million  654  thousand  321. 


10 


ADDITION. 


The  preceding  contains  only  nine  digits,  wliich  render  it 
sufl&cie»tly  large  for  young  students  or  common  business, 
although  it  may  be  extended  much  farther,  thus : 


Quintillions.  Quatrillions.     TrlUions,         Billions.  Millions.  Units. 

987,654;  327,241;  278,325;  256,148;  212,563;  652,324. 


addition: 

The  use  of  Addition  is  to  ascertain  the  amount  of  two  or 
more  numbers  when  put  together. 

RULE. 

1st.  Set  down  any  one  of  the  numbers  and  place  under 
j  it  all  the  rest  in  such  a  manner  that  units  may  stand  under 
!  units,  tens  under  tens,  hundreds  under  hundreds,  and  so  on^ 
'and  draw  a  line  under  the  last. 

2d.  Begin  at  the  right  hand  column  and  add  together  all 
the  figures  contained  in  that  column.  If  it  amounts  to  ten 
'  or  more,  set  down  the  right  hand  figure  and  carry  the  left 
hand  figure  or  figui-es,  which  add  to  the  next  line,  and  so 
!  proceed  till  adding  the  last  line.  Then  set  down  the  whole 
amount.  , 


EXAMPLES. 


(No.  1.)    (2.) 
S3-         m  ja- 


(3.) 

t-'    ti    ^ 


(4.) 


I- 


""^ 


w 


4 
4 
2 
2 


5  8 
4  1 

6  9 
2  5 


2  3  4 

1  2  1 
4  6  8 

2  2  4 


13  4  6 

7  2  12 
10  3  2 

8  10  3 


(5.) 

2  4  6  8 

17  5  5 

10  2  0 

12  8  0 


Ans.  12    188    1047    17693      65  2i^ 


"*g*jgt>?.y? 


ADDITION. 


m 


(6.)     (7.)       (8.)        (9.) 

123  2408  87561  42146 

422  6273  10420  23323 

631  2103  32619  13357 

246  4  3  12  31427  24557 

323  3102  61422  12787 


1645  18258  2  2  3449  116170 

(10.)  (11.)  (12.) 

2?  256312  4621 

410  80191  2300 

11224  4307  96131 

24795  779  1200  12 

36135  2  402  12 

87282  124800  900 


159868    418791    223976 

13.  Add  the  following  numbers,  viz :  14, 16,,23,  29,  80, 
31,  and  100,  and  tell  their  amount.  Ans.  293. 

14.  What  is  the  amount  of  36,  97,  125,  384,  1176  ? 

Ans.  1818.  * 

15.  Add  640,  79,  80, 100,  210,  450,  787,  21fand  2.     j 

Ans.  2869. ' 

16.  John  gave  Joseph  33  apples;  James  gave  him  91; 
Peter  gave  him  56 ;  Joel  gave  him  107 ;  and  David  gave 
him  95 ;  how  many  had  he  ?  Ans.  382. ' 

17.  A  person  went  to  collect  money,  and  received  of  one, 
man  $542 ;  of  another  654;  of  another  550;  of  another  787, 
and  of  another  3405.  I  demand  the  sum  collected.  Ans.  5938. ' 

18.  John  owes  to  one  man  $302;  to  another  540;  to: 
another  70 ;  to  another  2356,  and  to  another  999.  How ' 
much  does  he  owe  in  all  ?  Ans.  $4267. ! 

19.  John  and  Charles  went  to  collect  nuts;  when  they^ 
i^d  collected  a  quantity,  sat  down  to  count  them ;  when  one  '■ 
had  collected  276  and  the  other  196,  what  number  did  both '' 
of  them  collect  ?  Ans.  471. ' 

20.  Desired  to  purchase  a  suit  of  clothes  which  cost  as  1 
follows,  viz :  a  coat  $25,  a  pair  of  pantaloons  10^  a  waiaicoati 
6,  a  shirt  2,  and  a  paii*  of  socks  1.  What  is  the  cost  of 
the  wholo?  Ans.  $44. 

21.  A  butcher  bottght  of  one  man  25  hoad  of  cattle ;  of 


-au 


12 


MULTirLIOATION. 


another  16 ;  of  anotber  40,  aud  of  anotlier  9.     How  many 
did  lie  buy  in  all  ?  Ans.  89  head. 

22.  A  man  in  buying  cider  received  of  one  man  90  gal- 
lons; of  another  200  j  of  another  300;  of  another  400,  aud 
of  another  500.     How  many  gallons  did  he  buy  in  all  ? 

Ans.  1490. 

23.  A  gentleman  went  to  purchase  brandy,  and  bought 
of  one  man  125  gallons;  of  another  160;  of  another  190, 
and  of  another  210.  ^  IIcfw  much  did  he  buy  in  all  ? 

Ans.  685  gallons. 

24.  A  man  in  buying  corn,  received  of  one  person  400 
bushels;  of  another  500;  of  another  600,  and  of  another  700. 
How  many  bushels  did  he  buy  in  all  ?     Ans.  2200  bushels. 


MULTIPLICATION. 

When  the  multiplier  does  not  exceed  12,  work  by 

RULE  I. 

Set  the  multiplier  under  the  right  hand  figure  or  figures 
of  the  multiplicand :  then  beginning  with  the  units,  multiply 
aU  the  figures  of  the  multiplicand  in  succession,  and  set 
down  the  several  products ;  but  if  either  of  the  products  be 
more  than  §.  set  down  its  right  hand  figure  only,  and  add 
its  left  hand  figure  or  figures  to  the  next  product.  The 
whole  of  the  last  product  must  be  set  down. 

pROor.  Divide  the  answer  by  the  nmltiplier,  and  the 
quotient  will  equal  the  given  sum. 

MULTIPLICATION  TABLE. 
The  learner  should  commit  the  following  tabic  to  memory 
before  he  proceeds  further : 


Twice 

1  make  2 

2  4 

6 


4 

5 

0 

7 

H 

0 

10 

11 

12 


8 
10 
12 
14 

10 

18 
20 
22 
24 


3  times 

1  make  3 

2  6 


3 
4 
5 
6 
7 
8 
0 
10 
11 


9 
12 
15 
18 
21 
24 
27 
30 
33 
36 


4  times 

1  make  4 

2  8 


8 

4 

5 

6 

7 

8 

9 

10 

11 

12 


12 

16 
20 
24 
28 
32 
86 
40 
44 
48 


5  times 

1  make  5 

2  10 


3 

4 

5 

6 

7 

8 

9 

10 

11 

12 


15 

20 
25 
30 
35 
40 
45 
50 
55 
60 


6  times 

1  make  6 

2  12 


3 
4 
6 

6 

7 

R 

9 

10 

11 

12 


18 
24 
30 
36 
42 
48 
54 
60 
66 
72 


7  times 

1  make  7 

2  14 


3 

4 

5 

6 

7 

8 

9 

10 

11 

12 


21 

28 
35 
42 
40 
56 
63 
70 
77- 
84 


JX 


MULTITlitCATION. 

13 

8  times 

1  make  8 

2  16 

3  34 

4  32 

5  40 

6  48 

7  56 

8  64 

9  72 

10  80 

11  88 

12  96 

9  times 

1  make    9 

2  18 

3  27 

4  36 
5-          45 

6  54 

7  63 

8  72 

9  81 

10  90 

11  99 

12  108 

10  times 

1  make  10 

2  20 

3  30 

4  40 

5  50 

6  60 

7  70 

8  80 

9  90 

10  100 

11  110 

12  120 

11  times 

1  make  11 

2  ^22 

3  S3 

4  44 

5  55 

6  66 

7  77 

8  88 

9  99 

10  110 

11  121 

12  132 

12  times 

1  make  12 

2  24 

3  36 

4  48 

5  60 

6  72 

7  84 

8  .       1)6 

9  108 

10  120 

11  132 

12  144 

(  i.)    412  multiplicand. 
2  multiplier. 

^         824  product. 

(2.) 
Ans.  1 

5498 
3 

(3.)   12347 
4 

Ans.  49388 

6494 

(4.)  12^49172      ( 

5 

5.) 
5 

98754 
6 

(6.) 

12345678910 

7 

.      .,    61745860 

92524 

86419752370 

(7.)  64115928      ( 
8 

8.)  21938      (9.) 
9 

197442 

98765432144 
10 

■          512927424 

987654321440 

(10.) 

5324786 
11 

(11. 

Ans. 

)    84532911 
12 

Ans. 

58672646 

1014394932 

'    (12.) 

148100076 

3 
3 

9 

(13.).  1 
Ans.  3 

50000000000 

2 

}       Ans. 

444800228 

00000000000 

'1  <^''-) 

110008191 
4 

(15.) 
Ans. 

987554321 
2 

J       Ans. 

440032764 

1975108642 

!i    (16) 

17853440 
5 

(17.) 

1888880000 
5 

Anp. 

89267200 

Ans. 

9444400000 

^ 

2 


14  MULTIPLICATION. 

(18.)  1280721         (19.)  9922446688 
3  4 


Abb.  8692163  Ans.  39689786752 

(20.)  6001150084S211 

7 


Ana.  420080505902477 


21.   Multiply  21141   by   2  Auawcr  42282 

22 73211 3 219633 

23 87092 4 350768 

24 95698 5 478490 

25 91144 6 546864 

26 83456 7 584192 

27 21110 8  ........  168880  • 

28 34000 9 806000 

29 10056 10 100560 

30 -. .  20000 11 220000 

31 800510 12 9606120 

When  the  multiplier  excjeeds  12,  work  by 

RULE  n. 

l^Iultiply  by  each  figure  separately.  First  by  the  one  at 
the  right  hand,  then  by  the  next,  and  so  on,  placing  their 
rebpective  productH  one  under  another,  with  the  right  hand 
figure  of  car-h  produot  directly  under  that  figure  of  the 
muUipKcT  by  which  it  in  produced.  Add  these  product* 
together,  and  their  amount  will  bo  the  answer. 

SXAMFLKS. 

(32.)     120  multiplicand.  (33.)     1461 

14  multiplier.  16 

480  8706 

120  1461 

Am  1680  Ana.  23216 


ir 


MULTIPLICATION.  15 

(34.)       124680  (35.)    468 

^  142  72 


^ 


249360  9^»6 

498720  3276 

124680  ^5^ 


17704560 

86.  Multiply  4875   by   29   Answer  141375 

37 11271 36 394485 

38 19004 305 5796220 

39 .  :. :. . ; 76976  ...... .489 37641264 

40. 84769 976 82734544 

41 1978987 4809 9516948483 

JVoie,  When  there  are  ciphers  at  the  right  of  either  tho 
multiplicand  or  multiplier,  multiply  as  in  the  preceding  case, 
only  omitting  the  ciphers.  Then  add  together  the  several 
products,  and  place  to  the  right  of  the  amount  as  many 
ciphers  aa  are  to  the  right  of  both  fiactors.  - 

EXAMPLES. 

(42.)    Multiply    400      by      200      Answer  80000 
200 

80000 

43 8000 400 3200000 

44 3700 200 740000 

45 4870 2500 12175000 

46 876956 990000. . .  .868186440000 

JSTote.  When  the  multiplier  exceeds  12,  and  is  the  exact 
product  of  any  2  factors  in  the  multiplication  table,  the  op^ 
ration  may  be  performed  thus : — Multiply  the  given  sum  by 
one  of  eaid  factors,  and  that  product  by  the  other  factor. 

EXAMPLES. 

(47.)    MuUiply    2851     by    15     3  times  5  are  15 
3 


8558 


Ans.  42765 


SUBTRACTION. 

48.  Multiply   476  hy      25   Answer  11.900 

49 769G 81 623376 

50 8976 48 .430848 

51 87698 72 6814256 

52 20784 108 2244672 

53 81207 182 10719324 

54 47696 144 6868224 

55 75687 56. ..... ..  4238472 

56 ..... . .'. ; ...34075 36 1226700 

PRACTICAL   EXAMPLES. 

57.  A  man  has  25  stables,  and  in  each  stable  there  are  five 
horses,  how  many  has  he  in  all  ?  An8.  125. 

58.  A  man  has  four  chests,  and  in  each  chest  there  are 
four  dollars,  how  many  dollars  are  there  in  all?      Ans.  16. 

59.  Josiah  has  30  apples,  and  James  has  six  times  tliat 
number,  how  many  has  James  ?  Ans.  180. 

60.  A  man  has  three  tracts  of  land,  each  containing  52 
acres,  how  many  acres  has  he  in  all  ?  Ans.  156. 

61.  A  laborer  hired  himself  for  six  years,  at  ^75  per  year, 
''  how  much  did  he  receive  for  the  six  years'  labor  ?  Ans.  $450. 

62.  A  certain  potato  field  is  90  hills  in  length,  and  breadth 
100,  how  many  hills  are  there  in  the  field?         Ans.  9000. 

63.  A  certain  cornfield  is  98  hills  in  length,  aiid  10  in 
breaxlth,  how  many  hills  are  there  in  the  field  ?  *  Ans.  980. 

64.  A  man  ha\'ing  built  a  house,  found  he  had  used 
18,175  bricks,  how  many  bricks  will  be  necessary  to  build 
14  houses  of  the  same  size  ?  Ans.  254450. 


SUBTRACTION. 

^    Subtraction  is  used  to-  know  the  difference  between   a 
larger  and  smaller  number. 

RULE. 

Set  down  the  larger  number  first,  and  under  it  with  units 
under  units,  tens  under  tens,  the  smaller.  Then  begin  at 
the  right  hand  or  unit's  place,  and  take  the  lower  figure 
from  the  one  above  it,  if  the  upper  figure  be  more  than  the 
lower,  and  set  down  the  remainder.  But  if  the  upper  figure 
be  less  than  the  lower,  add  10  to  the  upper  figure,  take  the 
lower  figure  from  the  amount^  set  down  the  remainder,  and 
carry  one  to  the  next  lower  figure. 


rnc 


SUBTRACTION. 


17 


!| 


PiiooF.  Add  the  lower  number  and  tte  answer  together, 
and  their  amount  will  equal  the  upper. 


(1) 


From 
Take 


EXAMPLES. 

964 


,  3. 
4. 
5. 

6; 
/ . 

8. 

9. 
10. 
11. 


Ans 

From  487 

875 

967 

1001 

9705 

87696 

455692 

1000000 

10000 


333 
631 


(2.) 


841 
579 


Take    96 

302 

351 

4J87 

1307 

10091 

300120 

1 

9 


Ans.  262 

Ans.  391 
573 


616 
514 

8458 

77605 

155572 

999999 

9991 

How  Kany  more 

Ans.  20. 

IIow  mnny 

Ans.  17. 

He  has  now 

Ans.  $<)2. 

had  §1000,  but  has  lent  105.     How 

Ans.  !i?895. 
After  I  pay  $69,  how  much  will  I  still 

Ans.  $491. 


12.  JaiiiCR  ha,s  44  apples,  and  John  24. 
has  James  than  John  ? 

13.  Henry  has  25  marbles,  and  Charles  8 
more  has  Henry  than  Charles  ? 

14.  William  holds  Jesse's  note  for 
paid  $37.     How  much  does  he  still  owe? 

'      15.   A  merch;iiit 
much  has  he  left? 

16.  I  owe  $560. 
owe? 

17.  A  merchant  had  180  yards  of  cloth,  but  sold  75. 
How  many  had  he  left  ?  Ans.  105  yds. 

18.  A  farmer  had  999  acres  of  land,  but  has  given  his 
son  500.     How  much  has  he  left?  Ans.  499  acres. 

19.  There  are  two  piles  of  bricks.  In  tl^e  greater  pile 
there  are  7896,  and  in  tlie  less  4389.  How  many  more  arc 
there  in  the  greater  pile  than  in  the 'less?  Ans.  3507. 

20.  A  merchant  bought  4875  bushels  of  wheat,  out  of 
which  he  sold  2976  bushels.  How  many  bushels  had  he 
left?  Ans.  1899  bushels. 

21.  I  deposited  in  bank  $1240.  I  have  since  taken  out 
S1082.     How  much  remains?  Ans.  $158. 

22.  A  farmer  had  5487  acres  of  land.  He  sold  to  A  325, 
to  B  750,  and  to  G  1000  acres.     How  many  had  he  left? 

Ans.  3412  acres. 


18  8II0RT  DIVISION. 

23.  I  had  1200  pounds  of  pork,  and  sold  to  one  ma?i  400, 
to  another  350,  and  to  another  125.     How  much  was  left  ? 

Ans.  325. 

24.  In  a  certain  milk  house  there  were  44  crocks  of  milk, 
but  it  so  happened  an  unruly  cat  broke  in  and  destroyed  19. 
How  many  were  left?  Ans.  25. 

25.  In  a  certain  baiTcl  are  04  gallons  of  wine.  If  20  be 
di-awn  out,  how  many  will  be  left  ?  Ans.  74. 

26.  A  ship's  crew  consisted  of  75  men,  21  of  whom  died 
at  sea.     How  many  arrived  safe  in  port  ?  Ans.  54. 

27.  A  tree  had  647  apples  on  it,  but  158  of  them  fell  off. 
How  many  were  there  then  remaining  on  the  tree  ? 

Ans.  489. 

28.  I  saw  15  ladies;  8  returned  back.  How  many  passed 
on?  Ans.  7. 

29.  A  general  had  an  army  of  43^50  men ;  15342  of  them 
deserted.     How  many  remained  ?  Ans.  27908. 

30.  A  man  starting  a  journey  of  950  miles.  When  he 
may  have  gone  348  miles,  how  far  has  he  still  to  go? 

Ans.  602  miles. 

31.  A  trader  had  655  bogs;  99  of  them  were  stolen;  24 
died  of  sickness;  he  then  sold  400.  How  many  had  he 
left?  Ans.  132. 

SHORT  DIVISION. 

By  Division  we  ascertain  how  often  one  number  is  con- 
tained in  another.  The  number  to  be  divided  is  called  the 
dividend.  The  number  to  divide  by  is  called  the  divisor. 
The  number  of  times  the  dividend  contains  the  divisor  is 
called  the  quotient.  If  on  dividing  there  be  a  remainder  it 
is  called  the  overplus. 

RULE. 

Place  the  divisor  to  'the  left  of  the  number  you  wish  to 
divide.  Consider  how  many  times  the  number  by  which 
you  wish  to  divide  is  contained  in  the  first  figure  or  figures 
of  the  number  to  be  di^'ided,  and  set  down  the  result, 
noting  whether  there  be  any  remainder.  If  there  be  no 
remainder,  consider  how  often  the  divisor  is  contained  in  the 
next  figure  or  figures;  but  if  there  be  a  remainder,  con- 
ceive it  to  be  placed  to  the  left  of  the  next  figure;  into 
which  divide  as  before,  and  set  down  the  result. 


SHORT  DIVISION. 


19 


Proof.  Multiply  the  quotient  by  the  divisor ;  add  in  the 
remainder,  if  any.     The  product  will  equal  the  dividend. 


EXAMPLES. 


(1.)    Divide  836  by  3 
3)386 


(3.) 


(5.) 


(7.) 


0. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 


Ans.  112 
2)4681278 

2340639 
4)1896481 

474107  -f  3 
6)9654630 

1609105 

Divide    8767 

—  9698 

—  97899 

—  80409 

—  981021 

—  . 897697 

—  9876978 

—  4967844 


(2.)    Divide    448  by  2 
2)448 

Ans.;  224 
(4.)    3)63912964 


(6.) 


21304321 
5)863200 


by 


5 
'6 

—  7 

—  8 

—  9 

—  10 

—  11 
--  12 


172640 
(8.)    7)1269503450 

181357635  -f  5 
Answer 


1753  +  2 

1616  +  2 

13985  +  4 

10051  +  1 

109002  +  3 

89769  +  7 

897907  +  1 

413987 


17.  Di\T[de  336  pounds  of  sugar  equally  among  3  boys? 

Ans.  112. 

18.  Divide  1284  pounds  of  cotton  equally  among  4  girls  ? 

Ans.  321. 

19.  Divide  8655  acres  of  land  equally  between  2  heirs  ? 

Ans.  4327: 

20    Bought  6  horses  for  318  dollars.     How  much  did 

each  cost  ?  Aus.  53  dollars. 

21.  John  would  divide  120  ears  of  corn  among  10 
horses.     What  was  the  share  of  each  ?  Ans.  12. 

22.  Divide  1200  pounds  of  coffee  among  12  womcu? 

Ans.  105. 

23.  I  would  divide  8880  apples  among  8  boys.     What 
was  the  share  of  each?  Ans.  1110. 


^ 


20  LONG   DIVISION. 

LONG  DIVIsiON. 

Long  Division  is  used  when  the  divisor  exceeds  12. 

RULE. 

Place  the  diviboi*  to  the  left  of  the  dividend,  as  in  short 
division.     Consider  how  often  the  divisor  is  contained  in 
j  the  least  number  of  figures  into  which  it  can  be  divided,  and 
i  set  down  the  result  to  the  right  of  the  dividend.     Multiply 
;|  the  figures  set  at  the  right  of  the  dividend  by  the  divisor, 
and  set  the  pi-oduct  under  the  figure  in  which  you  con- 
sidered how  often  the  divisor  was  contained.     Subtract  the 
product  from  the  line  above  it,  and  set  down  vs^hat  remains, 
which  must  always  be  less  than  the  divisor.     Bring  down 
the  next  figure  to  the  right  of  the  remainder,  and  proceed 
as  before,  till  all  the  figures  of  the  dividend  are  brought 
down.     When  there  are  ciphers  at  the  right  of  both  factors, 
the  operation  may  be  shortened  by  cutting  off  an  equal 
number  of  ciphers  from  each. 

EXAMPLES. 

(1.)  Divisor  24)480  di^ddend.   Ans.  20. 

-   48 

0 
(2.)   25)450    Ans.  18. 
25 

200 

,.   200 

3.  Divide  456  by  21  Ans.  21  Remainder  15 

4.  861    19      19 

5.  958    18      53        4 

6.  12350    15      823        5 

7.  1475    28      52        19 

8.  4277    31      137        30 

9.  25757    37      696        5 

10.  256976    41     6267        29 

11.  997816    59    16912         8 

12.  4697680424   125  37581443        49 

13.  9924000  54000      183        42 

14.  74000000  3700    20000 


LONG 


15  Divide  80906000  by  180  Ans.  449477  Remainder  14 

16.  555555555  55555  10000  5555 

17  3875642  7898  490  5622 

18  98765432  1234  80036  1008 
19*  •  12486240  87654  142  39372 
20  57289761  7569  7569 
2l'  99007765  27000  3689  4765- 
22!  15463420  1600  9664  1020 

PRACTICAL   EXAMPLES. 

23.  If  18G0  pounds  of  beef  be  divided  equally  among  60 
men,  what  will  be  the  share  of  each?         Ans.  31  pounds. 

24.  4556  pounds  of  salt  are  to  be  equally  divided  among 
an  army  of  44  men.     AVhat  will  be  the  share  of  eacli  man  ? 

^  Ans.  103  +  24. 

25.  4006  pounds  of  malt  are  to  be  divided  equally  among 
an  'ivmv  of  84  men.     What  will  be  the  share  of  each  man  y 

^  Ans.  47  -1-  58. 

26.  1600  bushels  of  corn  are  to  be  divided  equally  among 
40  men,  how  much  is  that  a  piece  ?  Ans.  40. 

•  27.  A  regiment  consisting  of  500  men  are  allowed  1000 
pounds  of  pork  per  day.     How  much  is  each  man's  part  ? 

Ans.  2  lb. 

28.  If  a  field  of  32  acres  produce  1920  bushels  of  corn, 
how  much  is  that  per  acre?  ^         Ans.  60  bushels. 

29.  A  prize  of  $25526  is  to  be  equally  divided  among 
100  men.    What  will  be  each  man's  part?  Ans.  8255  +  26. 

30.  How  many  horses,  at  $30  per  head,  may  be  bought 
for  $38040?  Ans.  1208. 

31.  If  a  field  containing  25  acres  produces  37o  bushels 
of  wheat,  how  mmk  docs  one  acre  produce  ? 

Ans.  15  bushels. 
.  32.  96  persons  are  to  have  480  pounds  of  beef  divided 
equally  among  them.     What  is  the  share  of  each? 

Ans.  5  pounds. 

33.  144  men  are  to  pay  equal  shares  of  a  debt  which 
amounts  to  $144000.  How  much  must  each  man  advance 
to  make  up  the  sum?  Ang.  $100. 

34.  If  $2400  be  equally  divided  among  16  persons,  what 
will  be  the  share  of  each?  Ans.  $150. 

85.  A  man  gave  35  reapers  $385,  each  to  have  an  equal 
I  part.     How  much  did  each  man  receive  ? Ans.  Sll. 


22  LONG  DIVISION. 

86.  A  man  travelled  560  miles  in  40  days.  How  far  was 
that  in  one  day  ?  Ans.  14  miles. 

37.  A  boy  hired  60  days,  for  which  he  was  to  receive 
$120.     How  much  was  one  day's  labor  worth  ?       Ans.  $2. 

38.  When  I  have  labored  60  days  for'  the  sum  of  '$180, 
how  much  is  one  day's  labor  worth  at  that  rate  ?     Ans.  $3. 

EXAMPLES  TO  TRY  THE  STUDENT  IN  ORDER  THAT  HE  MAY 
UNDERSTAND  THE  FOREGOIN(J  RULES,  VIZ  :  ADDITION, 
MULTIPLICATION,  SUBTRACTION  AND  DIVISION. 

39.  John  had  40  apples.  He  gave  his  brother  10 ;  kept 
10 ',  and  divided'  the  rest  equally  between  his  two  sisters. 
How  many  had  each  sister  ?  Ans.  10. 

40.  John  owes  James  ^50.  Peter  owes  him  $80.  David 
owes  him  $105.  Samuel  $91.  Eli  $7.  And  Joseph  $40. 
After  James  collects  the  above  debts  and  pays  $99,  which 
he  owes,  how  much  will  he  have?  "  Ans.  $274. 

41.  A  farmer  has  three  tracts  of  land,  ejieh  containing  20 
acres ;  buys  an  adjoining  one  of  90  acres.  If  he  sell  40 
acres,  and  divide  the  rest  equally  between  his  two  sons, 
what  will  be  the  share  of  each  ?  '  Ans.  65. 

42.  A  person  has  50  sheep ;  buys  from  his  neighbor  50 
more  J  he  then  sells  25  to  the  butcher.  How'many  has  he 
left?  '  Ans.  75. 

43.  A  gentleman  dying  left  $2500,  to  be  divided  as  fol- 
lows; To  his  son  1500  dollai'S,  and  the  rest  equally  between 
his  two  daughters.     How  much  did  each  daughter  receive  ? 

Ans.  500  dollars. 

44.  A  person  went  to  collect  money,  and  received  of  one 
man  800  dollars;  of  another  50;  of  another  18;  of  another 
440,  and  of  another  25.  After  which,  by  gambling,  he  lost 
103  dollars.    How  much  had  he  left  ?     Ans.  1230  dollars. 

45.  Suppose  a  certain  field  be  140  hills  in  length,  and 
124  in  breadth.  Admit  there  be  two  stalks  in  every  hill, 
and  on  each  stalk  an  eai'  of  corn,  how  many  bushels  are 
there  in  the  field,  suppose  100  ears  to  make  a  bushel  ? 

Ans.  347  bushels  +  20. 

46.  Bought  25  yards  of  fine  cloth  for  250  dollars.  How 
mnch  was  it  per  yard  ?  Ans.  10  dollars. 

47.  Bought  16  loads  of  hay  at  4  dollars  per  load.  What 
did  it  amount  to  ?  Ans.  64  dollars. 


TABLES   OF   WEIGHTS   AND   MEASURES.  23 

48.  How  many  yards  of  cloth,  at  6  dollars  per  yard,  can 
I  have  for  90  dollars  ?  Ans.  15  yards. 

49.  How  many  pair  of  gloves,  at  1  dollar  per  pair,  can  I 
have  for  4  dollars  ?  Ans.  4. 


TABLES 

0£  MONEY,   WEIGHTS,   AND   MEASURES. 


FEDERAL  MONEY. 

The  denominations  are, 

10  Mills  (marked  m.)    make  1  Cent,     ct. 

10  Cents 1  Dime,   d. 

10  Dimes  (or  100  cts.)  .     .  1  Dollar,  D.  or  0 

*     10  Dollars 1  Eagle,  E. 

AVOIRDUPOIS  WEIGHT. 

Th*e  denominations  are, 

16  Drams  (marked  dr.)  make  1  Ounce,     oz. 

16  Ounces 1  Pound,     lb. 

28  Pounds 1  Quarter,  qr. 

4  Quarters  (or  112  lbs.)  .     1  Hundred  weight,  ewt. 
20  Hundred  weight  ...     1  Ton,        T. 

TROY  WEIGHT. 

The  denominations  are, 

24  Grains                   make       1  Pennyweight,  dwt. 
20  Ponnywcights       ...     1  Ounce,      '      oz. 
12  Ounces 1  Pound,  lb. 

« 

APOTHECARIES  WEIGHT. 

The  douomiuatiou.s  arc, 

20  Grains  (gr.)        make        1  Scruple,  9 

3  Scruples 1  Dram,      3 

8  Drani.s J.  Ounce,     3 

12  Ounces 1  Pound,     ft 

JVote.  By  Avoirdupois  AVeight  are  weighed  all  things  of 
a  coarse,  drossy  nature ;  and  all  metals,  but  gold  or  silver, 
by  Troy  Weight.  Jewels,  gold,  silver,  and  Tupiors,  arc 
weighed  by  Apothecaries  Weight.  Apothecaries  mix  their 
medicine  byTroy,  but  buy  and  sell  by  Avoirdupois  Weight. 


ime 


24 


TABLES   OF    WEIGHTS   AND    MEASURES. 


LONG  MEASURE. 

The  denominations  are, 

12  Inches  (m.)  make  1  Foot,  ....        ft. 

3  Feet i  Yard,        .     .     .       yd. 

5  J  Yards  (or  16^  feet)    .     .  1  Rod,  pole,  or  porch,  P. 

40  Poles  (or  220  yds.)      .     .  1  Furlonr,  .     .     .     fur. 

8  Furlongs  (or  1760  yds,)  .  1  Mile,    ....       M. 

3  Miles 1  League,     ...        L. 

60  Geosraphic,  or )     .,  t  t\  / 

69jS0,tuli  }™'^^      •    l»«g^«.     •    ■    •     •^'^- 

360  Degrees  the  circumference  of  the  Earth. 

LAND  OR  SQUARE*  MEASURE.  " 

The  denominations  are, 
144  Square  inches  ( 

9  Square  feet   . 
30.1  tScjuare  yards 
.40  Square  perches 

4  Roods      .     . 
f>40  Acres       .     . 


CLOTH  MEASURE. 

Tlie  denominations  are,  ^ 

2^^  Inches  (in.)         make  1  Nail,     ....       na. 

4  Nails 1  Quarter  of  a  yar'd,       qr. 

4  Quartern 1  Yai-d,     ....        yd. 

8  Quarters 1  Ell  Flemish,  \      E.  Fl. 

T)  Quarters 1  Ell  Enjili^h,    .     .  E.  E. 

6  Quarters       ....".  1  Ell  French,     .     .  E.  F. 


in.)    make 

1  S<|uare  foot,   .     .       //. 
1  Square  yard,  .     .       yd. 
1  Rod,  pole,  or  perch,"*  P. 
1  Rood,  ....        R. 

1  Acre,    ....        ,3. 

1  Square  Mile,  .     .       M. 

LIQUID  MEASURE. 

The  denominations  arc, 

4  Gills  (gL)  makfe  1  Pint,  . 

2  Piiit.s 1  Quart,  . 

I  (Jallon,  . 


is; 


4  C^udi'lrf 

31^  Gallons 1  l^arrel, 

63  Gallons 

2  Hogsheads 1  Pipe  or  butt, 

2  Pipes  (252  gal.  or  i  hhds,)  1  Ton,       .     . 


2>L 

ql. 

bar. 
hhdl 
P.  or  B. 
T 


COMPOUND  ADDITION.  26! 

I  DRY  MBASLRE. 

The  denominations  are, 

2  Pints  (pt.)        make         1  Quart,         qt. 

8  Quarts 1  Peck,         pe. 

4  Pecks 1  Bushel,      bu. 

J\rote.  Long  Measure  is  used  for  measuring  lengths,  dis- 
tances, etc.  Land  or  Square  Measure  is  used  for  measuring 
lands,  &c.  Cloth  IMcasure  is  used  for  measuring  cloth, 
tape,  &c.  Liquid  Measm-e  is  used  for  measuring  vinegar, 
rum,  brandy,  wine,  cider,  perry,  oil,  &c.  And  Dry  Measure 
is  used  for  measuring  grain,  fruit,  salt,  &c. 

TIME. 

The  denominations  are, 
60  Seconds  (sec.)        make  1  Minute,   min. 

60  Minutes 1  Hour,  hr. 

24  Hours 1  Day,  da. 

7  Days 1  Week,  w. 

52  Weeks,  1  day  and  6  hours,  or  )  ,  v- 

365  Days  and  6  hours,                     J  ^  ^®^'  V' 

12  Calender  months     ....     1  Year,  y, 

^   13  Lunar  months 1  Year,  y. 

The  following  is  a  statement  of  the  number  of  days  in 
each  of  the  twelve  calender  months: 

Thirty  days  hath  September, 
April,  June  and  November; 
All  the  rest  have  thirty-one, 
Exoept  ihe  second  month  alone, 
Which  has  but  twenty-oight  in  fine, 
Till  leap  year  gives  it  twenty-nine. 


COMPOUND  ADDITION. 

Compound  Addition  consists  of  several  denominations. 

RUTiE. 

Set  the  numbers  of  like  denomination  under  each  other, 
leaving  a  space  between.  Then  begin  at  the  right  hand 
column,  and  add,  as  in  Simple  Addition.  Divide  the  amount 
by  as  many  as  will  make  one  of  thj  next  greater.  If  there 
be  any  remainder,  set  it  down  under  the  column  aaded.  K 
no  remaindei*,  set  down  a  cipher.     Carry  the  quotient  pro- 


26  COMPOUND  ADDITION. 

duced  by  dividing,  to  the  next  higher  denomination^  and  bo 
Iproceed. 

Proof.    Ah  in  Simple  Addition. 

J^oie,  In  adding  fractions,  count  i  one,  ^  two,-f  three, 
because  four  fourths  niaJke  a  Ts^holc  one.  Or  if  thirds,  count 
^  one,  •§  two;  because  three  thii-ds  make  ^  whole  one.  ', 

EXAMPLES.  ^.,  ,,    : 

(1.)  '$  cis.  (2.)  $  cts.  '(3.)  ^.$  ">«/«-i3 

5  XT  10  80  110 '50- 

1  JO  5  14  •   12  25 

^  50  .2  62  9  20 

8  44  1'  '  75  112  18 


Ans.  17'  -16  Ans.  19  81  Ans;  244  13 

(4.)  %    'Cts.  (5.)  $  els.  (6.)   $  cts. 

125  50  120  18|  910  31i 

812  30  56  25  16  18 

560  12  130  12  J  122  12  J 

12.  10  25  25  90  09 

i>  00  72  56  J  999  99 

,,80  01  1  09  125  06^ 


(5.)  $ 

Cts. 

120 

18| 

56 

25 

130 

12^ 

25 

25 

72 

56J 

1 

09 

Ans.  4Q5 

m 

.(?•)  .^-. 

/cU- 

24 

-m 

19 

37i 

50 

Ans.  1816  03    Ans.  4Q5  \rq       Ang.  2263  76 

(7.)  -t^  rtf^          (?.)  S-  Ms.  (9.)  S  cts 

500  00        24  "68f  40  00 

200  00        19  37  i  6  00 

150  00        22  50  2  00 

140  00  •      17  55  2  00 

130  00       10  37  i  2  00 

120  ^t]                1  06i  -8  75 

— ~         ,          o     i2|  1     12^ 

Ad-*.1240    621                ••■•■■----    ■^'  ''"W^7i 

Ans.- 97.   67^  ™ 

Ans.  58    25 

10.  Laid  out  in  market  for  cloth  12  dollars  50  cents;  for 
tobacco  20  dollars  75  cents ;  for  salt  13  dollars  50  cents ; 
for  calico  40  doikrs;  for  cinnamon  18  dollars  29 f  cents; 
and  for  sugar  90  dollars  22  cents.  How  much  did  the 
whole  asaoimt  to?  Aub.  195  dollars  26f  cents. 


COMPOUND  ADDITION.  27 

11.  I  have  bought  4  yards  of  lace  for  5  dollars;  a  veil 
for  8  dollars  50  cents ;  9  yards  of  silk  for  18  f^oljajcs  87  \ 
cents;  12  y^rds  of  ribbon  for  1  dollar  18  J  cents;  19  yards 
of  linen  for  14  dollars  50  cents ;  2  pair  of  gloves  for  87h 
cents  ;  3  pieces  of  domestic  for  5  ddiars  37J  cen|s ;  9  yards 
of  lace  for  7  dollars  87^  -cents,  and  6  yards  of  cambrick  for 
20  dollars.     What  did  the  whole  amount  to  ?    ' 

Ans.  82  dollars  18|  cents. 

12.  Bought  of  Buckner  Wiilingham,  cloth  for  a  coat,  for 
25  dollars ;  a  pair  of  pantaloons  for  12  dollars  50  cents  •  a 
vest  for  G  dollars  12 J  cents ;  a  hat  for  8  dollars  60  cents ; 
a  shirt  for  2  dollars;  a  cravat  for  1  dollar;  a  pair  of  socks 
for  1  dollar  50  cents;  a  p:^  of  boots  for  7  dollars  56 J  cents; 
a  pair  of  slips  for  1  dollar  25  cents;  a  pair  of  suspenders 
for  75  cents;  a  pair  of  gloves  for  1  dollar;  a  handkerchief 
for  1  dollar ;  and  a  great  coat  for  35  dollars.  What  did  the 
whole  suit  cost .?  An4.  103  dollars  10 J  cents. 

13.  A  gentleman  in  building  a  fine  house,  finds  his  plank 
costs  950  dollars;  his  workmen  will  have  1000  dollars; 
the  stone  will  cost  J60  dollars;  the  window  glass  40  dol- 
lars, boarding  his  hands  600  dollars.  What  is  the  cost  of 
the  whole  ?  Ans.  2850  dollars. 

14.  My  agent  has  bouglit  in  market  a  turkey  for  1  dollar 
87J  cents ;  a  pair  of  shoes  for  1  dollar  68|  cont^^ ;  a  liam 
of  pork  for  43J  cents;  a  quarter  of  venison  for,!  dollar 
37|  cents;  a  piece  of  beef  for  y3|  cents;  a.hog-for  56^ 
cents ;  a  quart  of  strawberries  for  37j  cents ;  some  lard  for 
31 J  cents;  and  a  peck  of  potatoes  for  12 J  cents.  What 
did  the  whole  amount  lo  ?  Ans.  7  dollars  Q8^  cents,  j 

16.  A  man  desirous  lo  set  up  a  store,  laid  out  monies  as  I 
follows,  viz :  for  cloth  650  dollars  91  cents/  for  iron  220 ' 
dollars;  for  calicoes,  &c.,  1200  dollars  5  cents;  sugar  90 
dollars  4Qi  cents;  coiiee  559  dollars  99J  cents;  nails  80 
dollars;  books  1000  dollars >ink-s;ands  40  dollars;  slates  GO 
dollars;  leather  100  dollars;  tobacco  96'|:]ollars;  blankets 
205  dollars  1  cent;  cinnamon  13  dollarsJst  cents;  oil  29 
dollars  19  cents;  steel  30  dollars  33^  cefits;  molasses  16 
dollars;  hats  109  dollars  4h  cents;  castings  400  dollars 
55  cents;  thread  75  dollars  71  i  cents;  and  for  rum  227 
dollars  37^  cents.     What  is  the  cost  of  the  whole  ? 

4i)S.  5204  dollars  8|  cente.  I 


»t<r<wrMw*— II 


28  COMPt  UND  ADDITION. 

AVOIRDUPOIS  WEIGHT. 

(16.)    T.  cwL  qr.    l?.       (17.)  T.  cwi.  qr.  lb.  oz. 

2     14     1       .')                  3      2     1.  5  6 

4  11    3"  4     12     378 

5  6    2    li>                 5      6    2  0  2 
1      3     1      (3                 4    19    0  27  15 


Ans.  13     16    0      {^       Ans.  18      0    3    12    15 

18.  Add  12t.  16cwt.  Iqr.  191b.  15oz.  114t.  lOcwt.  2qr. 
271b.  4oz.  13dr.  72t.  4cw  .  2qr.  241b.  14oz.  3di-.  176t.  15cwt. 
3qr.  41b.  15qz.  lldr.      Ans.  376L  7cwt.  2qr.  211b.  loz.  lldr 

19.  Add  139t.  19cwt.  3qr.  181b.  13oz.  lOdi-.  1754t.  lOcwt. 
2qr.  lUb.  2oz.  14dr.27t.  3cwt.  l^^b.  lloz.  13cwt.  13oz. 

Ails.  1922t.  6cwt..  2qr.  171b.  8oz.  8dr. 

20.  Add  20t.  2cwt.  2qr.  12t.  15t.  2qr.  arwi  2t. 

Ans.  49t.  3cwt. 

TROY  WEIGHT. 
Ih.  oz.  dwt,  IK      oz.  cwL  gr. 

(21.)    4    5      6  (22.)    185      2     19    20 

8    9    13  56      9    15      6 

14      7  ife     11      2     17 

5    8    11  385      0      8      5 

13      2  10      8      7     12 


21     6     19  2110       8     13     12 

23.  Add  71b.  9oz.  lldwt.  22gr.  161b.  4oz.  18dwt.  6gr, 
1631b.  7oz.  12dwt.  18gr.  171b.  13dwt. 

Ans.  2041b.  lOoz.  ISdwt.  22gr. 
34.  Add  101b.  5oz.  2dwt.  lOgr.  51b.  lOoz.  lOdwt.  2gr. 
221b.  9oz.  15dwt.  Igr.  8,;z.  lOgr.  31b.  4oz.  2dwt.  Igr. 

Ans.  431b.  loz.  lOdwt. 

25.  Add  121b.  lOoz.  2dwt.  3gr.  41b.  5oz.  8dwt.  19gr. 

131b.  7oz.  lldwt.  Ans.  301b.  lloz.  Idwt.  22gr. 

APOTHECARIES'  WEIGHT. 

(26.)  fe  3  3  a  (27.)  fe  3  3  9  (28.)  %  ^  Z  ^  gr. 

6  321  3213  10  9426 

12  817  6432  19  1644 

112  635  10  024  75232 

40  4  1  0  108  6  1  0  126  8  1  1    3 

2621  19  432  1122  2  3  8    1 


174  4  5  2         147  5  5  2         1286  3  6  0  16 


COMPOUND   ADDITION.         ,         ■  29 

'  29.  Add  161b.  loz.  Idr.  2sc.  12gr.  1751b.  lOoz.  5dr.  lOgr. 
3201b.  3oz.  Idi-.  logr.  lloz.  2dr.  3sc. 

Ans.  5131b.  2oz.  3dr.  Osc.  17gr. 
30.  Add  181b.  lloz.  7dr.  Isc.  19gr.  1261b.  7oz.  5dr.  2sc. 
15gr.  961b.  Idr.  3gi-. 

Ans.  2411b.  7oz.  6dr.  Isc.  17gr. 


LONG  MEASURE. 

(31.)    L,    M.  fur.     P.            (32.)    yd.  ft.  in. 

-       -'  2  14 

5  2  7 

6  0  11 
9  3  5 
1  1  1 


2 

4 

7 

10 

4 

6 

5 

1 

1 

3 

2 

20 

75 

9 

8 

25 

256 

0 

1 

16 

Ans.  3  46       1       0      32  26       0        4 

33.  Add  500L.  IM.  2fur.  20P.  1yd.  2ft.  4m.  UP.  1yd. 
3in.  IjM.  2fur.  29P.  lOin.  4fur.  2fur.  lOin.  1yd.  2ft.  3m. 

Ans.  501L.  OM.  3fLir.  23R  5yd.  Oft.  6in. 

34.  Add  462L.  IM.  7fur.  29P.  1yd.  1ft.  lOin.  IIP.  1ft. 
lO:^.  IL.  IM.  2fur.  28P.  1yd.  2ffc.  9in.  13P. 

Ans.  467L.  3fur.  IP.  4yd.  5in. 


CLOTH  MEASURE. 

(  35.)    yd.  qr.  na.  (36.)  yd.  qr.  na.  (37.)  E.E.  qr.  na. 

234  111  19     32 

5     15  222  423 

76    2     1"  3    3   .3  27    3     1 

21     1    2  5    4    2  14     1     4 


.  •   106     1     2  14    0    0  66     1    2 

88.  Add  19yd.  2qr.  3na.  14yd.  2qr.  32yd.  2na.  3qr.  Ina. 
142Yd.  3qr.  2ua.  Ans.  210vd3. 

39,  Add  20E.F.  2qr.  3na.  401KF.  3qr.  2na.  126E.F. 
5qr.  Ina.  782E.F.  Ans.  1330E.F.  5qr.  2na. 

40.  Add  2E.F1.  Iqr.  3na.  lE.Fl.  Iqr.  Ina.  3qr. 

Ans.  5E.F1. 


30  COMPOUND   ADDITION. 

LAND  OK  SQUAKE  MEA^UBE. 
(41.)  A;.^i2,  P.    (42.)   ^.  'J2/'jp!    (43.)^.   11. 


21 

P. 

.m 

10 

o 

12 

SO 

') 

18 

110 

I 

2<) 

l>2;i 

ij 

10 

39 

,87 

51 

e 

02 

1 

17 

17 

«8 

(1 

ns 

1P> 

3 

120 

12 

21 

1 

582 

1 

}S 

1 

1 

Aus.  40G     2     11  ^TI2'  2      2  105     0 

I    .44    Add  021iA.  211.  20?.  908A.  IH.iSOP.  173A.  3R. 
U:7f    inOUA-iR.  ITP.  '        Ana.  2703A.  IE.  28P. 

i     45.  Add  i)90A.  8K.  88r.lS21A.  14P.  25A.  SR.  19P. 
!  150 A.  211.  IIP.  aud  2000A.  Acs.  4997A.  111.  87P. 

I  ■     LIQUID  MEASURE.  -    . 

!      (  :G.)     T.  hhd.    gal      (47.)  hhd.  gal.    qt.    pt.     gi, 
!  4      18  2      19      0      0      1 

j  45  ;;  40  0  Olio 

I  75  1        2  8  17      2      0      2 

I  91  2  58  '  '  0  21      0      1      0 

\  ■             ^!7  :>       .r,  0  0      0      0      1 


804,     8      54  5      58      0      1      0 

48.' Add  kB'jHr.  l,oal.  Iqt.  Ipt.  Igi.  13gal.  2qt.  Opt.  8gi. 
ilUir.  2gal.  3qi. '2pt.  Ogi.  Igal.  '2{&.  Ipt.  Ogi.  6bar. 

...    .  „  ^Ana.  81]=^ar.  19gal.  2qt.  Ipt.  Ogi. 
49.  Add  3851ilid.  42gal.  Sqt.'lpt.  27hhd.  S6gal.  2qt. 
!Pi;i}Jid.  17^.  leSlihd.  47gal.  2qt.  Ipt.  2gi.. 
1  -  Ar.s.  7091ihd.  ISgal.  Oot.  Opt.  2gi. 


-|i  DRV  MEASURE. 

1  .    . ,  ,.,,.  J,.,,.  <;/.  (  51.)  h(.  fp,  qt.  jiL  (52.)  hu.  pc.  qt.  pt. 

^         87    2    1        .     50  2    7    1  85    1  .5    1 

rs2    8    2             G5  8    5    2  •       9G    3    40 

428    1    0.         1S5  I   2    0  191    2    3    1 

'af52-'S    1-         178  2    1    1  201    17    0 

■^857    0    2             90  8    4    0  909    3    5    1 

TiesT!'^       ieo""  i  5  o      i485  1  i~i 

53.  Add  144bu.  3pe.  2qilpt.  Ipe.  2qt.  8qt.  Ipt.  462bu.. 
'  J8pt\'  Ipt.  72bu.  5qt.  Ipt.  Ans.  680bii.  Ope.  Gqt.  Opt. 


COMPOUND   ADDITION.  83 


54.  Add  eObn.  Ipe.  Iqt.  Ipt.  41bii.  3pe.  4qt.  Opt  500bu. 
2pe.  7qt.  Ipt.  183bu.  Ope.  5qt.  Opt. 

Alls.  786bu.  Ope.  2qt.  Opt. 

TIME.       . 

(55.)  F.   M.  (b(y.}w.  da.    hr.min.(b1.')da,  lir.  mrn.sec. 

80     5            3     2      9     20            4     23  45     30 

12     3            15     10    30            1     12  14     16 

15     7            2     1      9    25            3     19  17     22 

20    8            3    3    15    57            2    00  00     10 


Ans.128  11  10    5    21    12  12      7     17     18 

§8.  Add  25y  7«>.  12y.  3m.  96y.  10m.  26j.  9ra.  lly. 
7m.  and  9y.  Ans.  lS2y.  Om. 

APPLICATION. 

59.  Bonglit  potatoes  to  the  amount  of  $37  50  ct^?. ;  corn 
to  the  amount  of  119  21 J  ct^.;  wheat  to  the  amount  of  ^Sl 
37*^  ct-s.     Wllat  is  the  cost  of  the  whole? 

Ans.  S138  08f  cents. 

60.  Bou-ght  pcppei'  to  the  ani|jiunt  of  $358  75  cents;  oil 
to  the  amount  of  $105  OOJ  cents;  molasses  to  the  amount 
of  $4  43 1  CoS.     What  did  the  whole  amount  to  ? 

Ans.  S468  25  cents. 

61.  Bouo'lft  6  pieces  of  linen;  the  fh'st  contains  57yds. 
2qr. ;  the  second  20yds.  oqr.  2na. ;  the  thii'd  45yds.  ]  qr.  ; 
the  fourth  32yds.  3qr.  Ina. ;  and  the  other  two  each  38yds. 
2qr.     What  number  of  yards  are  there  in  the  whole  ? 

Ans.  242yd.^.  Iqr.  3na. 
Qr^:  There  are  4  bags  of  com ;  the  first  contains  2bu.  2pe. ; 
the  second  3bu,  3pe.  5qt;  the  third  3bu.  Ipe.  3qt. ;  the 
fourth  2bu.  and  4qt.     IIosv  mucli_  is  in  tlie  four  bag.s  ? 

'  --^    •  Ans.  llbu.  3p«.  2qt 

63.  A  man  l^as  three 'fehns  j't^ev- first  contains.  142a.  2r. ; 
the  second  32a.  3r.  12]^!  •  the  third  108a.  3r.  18p.  How 
many  acres  are  there  in  ;rll  ?  Ans.  ■284a.  Or.  30p. 

64.  There  are  3  pieces  of  lape;  the  first  yiea^urcs  15yds. 
3qr. ;  the  r.econd  iSyds.  Iqr.  2na. ;  the  third  25yds.  3qr.  2na. 
How  many  yards  are  there  in  the  three  pieces  ?     Ans.  60yds. 

65.  If  a  man  on  a  journey,  travel  the  first  day  43m.  ofur., 
the  second  29ra.  34p.,  the  tliird  57m.  2fur.  32p.,  and  the 
fourth  12m.  3fui'.  18p.,  how  many  miles  did  lie  traTcl  in  the 
four  days  ?•  Ans.  142m.  2fnr.  4p. 


32  COMPOUND    MULTIPLICATION. 

66.  Suppose  a  man  to  have,  in  one  barrel  40bii.  3pe.  Iqt. 
of  wheat,  in  another  50bu.  6qt.  Ipt.,  in  another  41bu.  2pe., 
in  another  64bu.  5qt.,  in  another  6bu.  Ipe.,  in  another  19bu. 
Ipe.  2qt.  Ipt.,  and  in  another  65bu.  6qt.  2pt.,  how  many 
bushels  are  there  in  the  whole  ?  * 

Ans.  287bu.  Ipe.  6qt.  Opt. 

67.  Suppose  a  man  has  in  one  trunk  4871b.  lOoz.  ISdwt. 
22gr.,  in  another  5001b.  8oz.  lldwt.  lOgr.,  in  another  2341b. 
lloz.  lOdwt.  16gr.,  how  much  has  he  in  all  ? 

Ans.  12231b.  7oz.  Idwt.  Ogr. 

68.  A  physician  received  from  Baltimore  three  boxes  of 
medicine,  which  cost  him  as  follows,  viz. ;  the  first  box  $21 
321^  cts. ;  the  second  819  37^  cts. ;  the  third  $40  17|  cts. 
What  did  the  whole  cost?  Ans.  $80  87^  cts. 


COMPOUND  MULTIPLICATION. 

When  the  multiplier  does  not  exceed  12,  work  by 

BiJLE    I. 

Set  down  the  number  to  be  multiplied,  and  place  the  mul- 
tiplier under  its  right  hand  denomination ;  and  in  multiply- 
ing observe  the  same  rules  for  caj-rying  from  one  denomi- 
nation to  another,  as  in  Compound  Addition. 

JVo/e.  If  there  be  i  in  the  sum,  divide  the  multiplier  by 
4 ;  a  ^  by  2  ;  f  by  2  and  4 ;  a  ^  by  3 ;  or  if  there  be  a  frac- 
tion in  the  multiplier,  divide  the  sum  in  like  manner,  and  add 
ctieir  amount  to  the  sum  produced  by  the  whole  number. 

EXAMPLES. 

FEDERAL  MONEY. 

(1.)  $    cts,  (2.)  $     cts.  (S.)  $      cts. 

2    50  12    66i  22    12J 

2  4  6 


Ans.  5  00  Ane.  50  25  Ans.  132  75 

(4.)  $  cts.  (6.)  $  cts,  (6.)  8  cts 

26  18f  58  78|        125  06 

3  5  7 


Ans.  78  56i   Ans.  293  93f    Ans.  875  43f 


COMPOUND   MULTIPLICATION.  33 

3      cts.  $      els. 

7.  Multiply     58  06^     by     4     Answer     232  2G 

8.  25  87J^     8        203  00 

9.  565  62J    12        6787  50 

10.  112  lOi    10        1121  05 

11.  •     222  22J    11       2444  47J 

AVOIRDUPOIS  WEIGHT. 

(U.^T.ctoLqrJb.  (lS.yT.cwt.qr.lb.oz.dr.  fU.)  qr.lb.oz.dr. 
861  16      *      6  14  2752  •3  14  64 

3  4  8 


Ans.  24  19   0  20  26  18  1  1  4  8       -    28    3  2  0 

15.  Bought  eight  bags  of  sugar,  each  weighing  2cwt.  Iq. 
41b#    What  is  the  weight  of  the  whole  ? 

Ans.  18cwt.  Iqr.  41b. 

16.  Multiply  4cwt.  3qr.  171b.  by  11. 

Ans.  53cwt.  Sar.  191b. 

TROY  WEIGHT. 

j  (  17.)  lb.  oz.  dwt.  ( 18.)  lb.  oz.  dwt.  gr.  ( 19.)  lb.  oz.  dwL  gr. 
56  4   14  47   2    0     8  112  8      2  20 

2  3  5 

*i 

112   9     8  141   6    1     0  563  4    14    4 

20.  Multiply  961b,  9oz.  lldwt.  lOgr.  by  8. 

Ans.  7741b.  4oz.  lldwt.  8gr. 

APOTHECARIES'  AVEIGHT. 

(21.)  ft  3  3  9  (22.)  ft  3  3  9  gr.  (23.)  ft  3  3  9  gr. 

4  8  2  1     47  2  1  2  12     12  3  4  2  0 

5  7  12 


• 


Ans.  23  5  3  2     330  3  5  0  4    147  7  0  0  0 

24.  Multiply  671b.  6oz.  3dr.  2sc.  by  7. 

Ans.  4721b.  9oz.  Idr.  2sc. 

25.  There  are  9  parcels,  each  weighio^  1091b.  7oz.  6dr. 
2sc.  2gr.  what  is  their  weight  ? 

Ans.  9861b.  lOoz.  4dr.  Osc.  18gr 


34  COMPOUND   MULTtPLIOATIO*\. 

LONG  MEASURE. 

(26.)    Jyj.  Pur.  P.  (27.)     L.   M.  Pur.   P. 

1      3      86  3      2      1      28 

12  7 


17      6      32  26      0    -3      SC 

28.  Multiply  14M.  6Fur.  39P.  by  11. 

Adb.  162M.  1  Fur.  29P 

29.  Multiply  IL.  2M.  3Fiir.  IP.  1yd.  1ft.  2in.  by  2. 

Ans.  3L.  IM.  6Fur.  2P.  2yd.  2ft.  4in. 

CLOTH  MEASURE. 

(SO.)yd.qr.na.  (dl.)  E.E.qr.na,  (32.)*E.F.  jr.na. 
12    3    2  22    2    3  16    2    1 

4  6  8 


Ans.  51    2    e  135    1    2  131    0    0 

33.  If  20yd.  2qr.  3na.  be  multiplied  by  7,  what  number 
of  yards  will  there  be?  Ans.  144yd.  3qr.  Ina. 

LAND  OR  SQUARE  MJ]ASURE. 

(34.)j3.  iJ.  P.  (35.)^.  /J.  P.  (30.)^.  ii.  P. 

38  3  13     47  2  10     20  3  30 

2      %     5  9 


77  2  26    237  3  10     188  1  30 

37.  Multiply  40A.1R.19P.  by  12.  Ans.  484 A.  IR.  28P. 

38.  How  many  acres  will  7  teams  plough  in  one  day, 
allowing  them  lA.  3R.  39P.  each?     Ans.  18A.  3R.  33P. 

LIQUID  ilEASURE. 

(  39.)  hhds.galqt.  (40.)  T.  hhd.galqt.pt.  (  41 .)  hJid.galqt.pi. 
2     13   3  2    1    12  2  1  6    43  2  1 

4  *8  7 


8     55   0  18    1    38  0  0  46    53  1  1 

42.  Multiply  2T.  Ip.  40gal.  3qt.  Ipt.  by  6.    . 

Ans.  15T.  Ip.  Ihhd.  56gal.  Iqt. 

43.  Multiply  4T.  Ihhd.  lOgal.  Ipt.  by  10. 

[  '  Ans.  42T.  3hhd.  38g;il.  Iqt.jj 


COMPOUND   MULTIPLICATION. 


ai5 


DRY  MEASURE. 
(4'f.)    hu.    pe.  qt.  pL 

180     5    2     1 
8 


(45.)  iv.  pc.  at.  pi 
li:    2    7    1 


145a    2    4    0  38    0    6    1 

46.  Multiply  120bu,  :3po.  Oqt.  2pt.  by  4. 

Aus.  483bu.  0i>c.  Iqt.  Opt. 

47.  MuHiply  189bu.  3pe.  7qt.  by  7. 

Ans.  1329bu.  3pc.  Iqt. 

48.  Multiply  98bu.  O])©.  5qt.  Ipfc.  by  0.         .  . 

Ans.  883bu.  2pe.  Iqt.  Ipt. 

TIME. 

(49.)  Y.   M.       (50.)  F.  M  (51.)  F.    W:  D, 
3     11                   8    4  12     19    5 

3  6  2 


11      9  50    0 

52.  Multiply  49Y.  9M.  by  7. 

53.  i\Iultiply  19Y.  29Da.  by  9. 


24    39     3 
Ans.  348Y.  3M. 
Ans.  171Y.  261Da. 
When  the  multiplier  is  more  than  twelve,  and  is  the  ex- 
act product  of  two  factors  in  the  multiplication  tabic,  -s^ork 
oy  rule  2.     Multiply  the  given  sum  by  one  of  the  facte  vs; 
then  multiply  that  product  by  the  other  fact-or.    ' 


(  51.)  Multiply  66 


EXAMPLES, 

cts.   m. 
37     5  by  36 
6 


S 
(55.)  5 


cfs. 

09  by  M 


398     25     0 
6 

An;3.  2389     50     0 


57. 
58. 
59. 
60. 
61. 
62. 


06 

44 

12 

•     22 


Cl-<.  7)1. 

2:.  3 

18J 

12  5 

18  7 

24  9 


by  86 
56 
96 
42 
48 
81 


10     18 
8 

81    M 

S       ctfi.  '  n 

Ans.  2389     50  U 

2478     16  8 

1170    00  0 

929     25  0 

1256    97  6 

C095     16  9 


36 

COMPOUND 

MULTIPLICATION. 

' 

63.  20 

64.  10 

cts. 
08  J 
12.} 

by  108 
144 

Ans.  2169 
1458 

cts.      jn. 
00       0 
00       0 

A. 

65.  47 

66.  25 

R.      P. 

3      20 

2        8 

by    54 
30 

.9. 

2585 
766 

R.    P. 

1  I 

2  00 

67.      48 

F.      1\ 

7      25 

by    88 

Jtf. 

4307 

F.     P. 

7       0 

ft 

68.     .56 

3        3 
9        6 

by    84 

ft 

4772 

:5     o  ( 

3       0 

Wlien  the  multiplier  is  not  the  exact  product  of  any  two 
factors  in  the  multiplication  table,  work  by  rule  3.     Use  the 
two  factors  whose  product  coraes   nearest  the  multiplier; 
then  multiply  the  given  sum  by  the  number  which  supplies 
!  the  deficiency,  and  add  its  product  to  the  sum  produced  by 
the  two  factors. 

EXAMPLES. 

69,   Multi 

$      cts. 
ply    2       25 

m. ' 

4x2 
10 

*  by  52 

1 

22       54 

6 
5 

112      70 
4       50 

0 

8 

117      20 

8 

*Tcn  times  5  ma.Vc  50, 

and  2  su 

pplies  the  deficiency. 

70.  Multi 

71. 

72. 

73. 

74. 

75. 

76.  7cwt. 

77.  121b. 

$    cts.     m. 
ply  4     75       8  by  29 
7     87*             47 
28     683             r,8 
49     75               87 
94    181             31 
42     31i         ,    58 
3qr.  221b.  by  51. 
5oz.  8dwt  by  39. 

Ans.    137 

370 

1950 

4328 
2919 
2454 
Ans.  405cwt 
Ans.  4851b.  6 

cts.      m. 
98       2 
12* 
75 
25 
81i 
12^ 
.  Ifjr.  21b. 

oz.  12dwt. 

_,  .           ..1 

COMPOUND  MULTIPLICATION. 

78.  4m.  6f\ir.   21p.  by  87  An^.  418m.    7fur.  27p. 

79.50a.  2r.      5p.  34  1718a.   Or.      l(fe. 

80.  60bu.  2pe.    5qt.         43  2608bu.  Ope.    7qt 

81.  2hlid.  41gal.2q.lpt.  17  46blid.   14gal.2qt.lpt. 

When  ihe  multiplier  is  ^eater  than  the  product  of  any 
two  factors  in  the  multiplication  table,  work  by  rule  4. 

Multiply  continually  by  as  many  tens,  less  one,  as  there 
are  figures  in  the  multiplier.  Thou  multiply  the  product  of 
the  last  ten  by  the  left  hand  figure  of  the  multiplier.  If 
greater  than  1,  again  multiply  the  given  sum  by  the  units 
figure  of  the  multiplier  j  the  product  of  the  first  tcu  by  the 
tens  figure;  the  product  of  the  second  ten,  if  any,  by  the 
hundreds  figure,  &c.  Then  add  ike  producte  of  these  several 
figures  together  for  the  answer. 

9  cts.  $  cts.  m. 

(83.)  Multiply 2  02ix2by222.  (83.)1  11  2xlby511. 
10  10 

20  25X2  .  il  12  0x1 

10  10 


202  50  111  20  0 

2  left  hand  figure.  5 

406  00  556  00  0 

4  05  1  11  2 

40  50  11  12  0 


449  55  568  23  2 

$  cts,  $     cts, 

84.  Multiply    5  18f  by  326  Answer  1685  93} 

85.  1  56J  466  713  64 

86.  2  87J  576  1656  00 

87.  4  81i  679  2928  ISf 

88.  18  931  457  8654  43f 

89.  25  48i  879  22359  56i 

yd,  ft,  in.  yd.   ft.  in. 

90.  5   12  604  2716   0   0 

M.Fur.P.  J^.  Fur.P 

91.  25    3   18  1265  32170   4   10 


=SmE 


38  COMPOUND   SUBTRACTION. 

vd.  qr.  na.  yd.    qr.  na. 

02.  Multiply  2li    2   1  by  3204.     Am.  72290  1    0. 

APrLlCATlON.  \ 

98.  Sold  125  bunbels  of  wheat  at  22  centa  per  bushol  \ 
"What  did  it  amount  to  'i  Ans.  §27  50  cents,  i 

94.  Sold  60  bushels  of  applea  at  15  cents  i>er  bushel,  i 
What  did  th(,'y  amount  to '{  Ans.  $^.  f 

95.  If  I  buy  18  yards  of  cloth  at  10  cents  per  yard,  what  I 
must  I  pay  ?  Ant.  91  30  cents,  j 

96.  When  one  eord  of  wood  coyt  92  10  ccntc<,  what  will- 
be  the  prii'C  of  nine  cords  at  the  same  rate  ? 

Ans.  $18  00  centa. 

97.  Sold  5cwt  of  tobac<To  at  $12  50  eentii  per  cwt.,  what 
did  the  whole  ambunt  to  ?  Ans.  $62  50  cents. 

EXAMPLES. 

%   cts.  %  cts. 

(98.)  Multiply  10  62Jby4  (99.)  Multiply  5  12iby8 
4  8 


42  48  40  96 

2  2 


Ans.  42  50  40  98 

100.  Bought  24  bushels  of  wheat  at  SI  12*  cents  per 
buiihel.     What  did  the  whole  amount  to  ?  Ans.  §27. 

101.  Bought  44  bu.  of  ecru  at  37  J  centa  per  bushel. 
What  did  the  whole  eosti'  Ans.  n516  50  cents. 

102.  A  merchant  bought  tn  o  pit^:3  of  linen,  the  one  con- 
tained 38  }ardB  and  the  other  26  yardd.  What  did  the  two 
pieces  cobt  at  ??8  87A  cents  per  yard  't  Ans.  1^48. 

103.  What  cost  a  box  of  sugar  wwighing  106  lbs.,  at  15i 
cents, per  pound?  '         Ans.  16  16 i  cts. 

104.  What  ^vill  13  ^  gallons  of  molasses  come  to  at  40 
I  cents  per  gallon  'f  Ans.  ^  40. 

105.  How  muih  will  25  bushels  of  oats  come  to  at,  15 
'cents  per  bushel?  Ans.  $3  75  cente. 

COMPOUxND  SUBTKACTION. 

EULE. 

Place  the  numbers  under  each  other  which  are  of  the 
same  denomination :  the  less  always  being  under  the  greater. 


Ilwn  MIIMIB 


^ 


COMPOUND   SUBTRACTION.  39 

Begin  at  the  right  hand  figure,  and  if  it  be  larger  than  the 
one  above  it,  consider  the  upper  one  as  having  as  many  ad- 
ded to  it  as  make  one  of  the  next  greater  denomination. 
Subtract  the  lower  from  the  upper  figure  thus  increased,  and 
fiet  down  the  remainder,  observing  to  carry  one  to  b<.^  added 
to  the  next  higher  denomination,  and  ho  proceed. 
Proof  as  in  Simple  Subtraction. 

♦  EXAMPLES. 

FEDERAL  MONEY. 

$    cts.  m.  $  cts.  m,  $  cts.   m. 

(l.)5  54  7   (2.)1  50  2   (8.)  19  84  4 

2  10  5        28  4      10  18  9 


i) 


Ads.  3  44  2  1  21  8      §  65 

$      cts.  ^  cts.                    $  cts. 

(4.)  64  87i  (5.)  10  37i  (O.)IOO  00 

25  12J  5  06J        55  62^  [ 

89  75  5  811  44  37^ 

$  cts.  $  cts.  ^  cts. 

(7.)  45  64|  (8.)  30  30  (9.)  150  93| 

5  99J  1  12^  90  10 

39  65J       29  17^        60  83f 

10.  I  owed  8559  22^  cents,  but  have  paid  $148  50  ct« 
How  much  remains  unpaid?  •  Ans.  $410  72 J-  cent<». 

11.  .Lent  a  man  $400;  he  now  returns  $211  12  J  centR. 
How  much  does  he  still  owe  ?  Ans.  $188  87^  coi\ta. 

12.  A  merchant  had  in  his  desk  $500  87  J  ce*its,  but 
drew  out  $120  93  cts.  to  pay  a  debt.  How  much  had  he 
le^  in  the  desk  ?  Aiis.  379  dollars  94  J  cents. 

13.  I  had  303  dollars  6^  cents,  but  lent  9  dollars  91i 
cent^^.     How  much  had  I  left?      Ans.  293  dollars  15  cents. 

14.  From  $1000  take  1  mill.         Ans.  $999  99  cts.  9m. 

AVOIRDUPOIS  WEIGHT. 

cwt.  qr.     lb,  T.    cwt.  qr.  lb. 

(15.)  6     3      25  (16.)  28      3  I  27 

4     2      12  13      1  0  19 

Abb,  a      1      18  15     2      1      08     , 


40  COMPOUND  SUBTftACTIQN. 

17.  From  14t.  lOcwfc.  2qr.  lOlb.  take  lUb. 

Ans.  14t.  lOcwt.  2qr.  51b. 

18.  Bcught  400cwt.  of  sugar,  but  have  since  sold  2cwt. 
3qr.  141b,     What  quantity  remaina  ? 

Ans.  S97cwt.  Oqr.  141b. 

TROY  WETGIHT. 

lb.    ox.  dwt.  g-^.  IbT     oz.   dwt.  gr. 

(19.)  24  6  19  18    (20.)  13   9   5  22 

19  5  18  23         8  11  16  10 


Am.  5  1   0  14         4   9   9  12 

21.  ProM  271b.  9oz.  16dwt.  take  19dwt. 

Ans.  271b.  8oz.  17dwt. 

22.  Subtract  lib.   Ooz.  17dwt.    15gr.   from  151b.   9oz. 
18dwt.  8gr.  Ads.  141b.  9oz.  Odwt.  17irr. 


APOTHECAEIES'  WEIGHT. 

f.       33  ft539  fe339 

(28.)  186    7  5    (24.)  96    4  02    (25.)  1009  82 

67    8  4  75    4  2  1  99  8  3  2 


Ans.  118  11  1  20  11  6  1  115  0 


CLOTH  MEASURE. 

yds.  qr.  na.          .     yds.  qr.  na.  yds.  qr,  na. 

(26.)  160    3    3      (27.)  969    2    1  (28.)'l4    0    3. 

37    12                786    1    2  9    3    2 

.1.1.1.  fti— 

A»s.  123    2    1                183    0    8  4    11 

'•A  t  >'•'■■ 

29.  Bought  27  yards  of  domestic,  but  have  since  sold 

9yds.  3qr.     How  much  remains?  Ans.  17yds.  Iqr. 

E.E.  qr.  na.              E.Fr.qr.  no.  E.Fr.qr.  na. 

(80.)  44    3    2       (81.)  62    2    3  (32.)  27    5    2 

1^3    3    1                  43    3    2  19    3    3 

Ans.  21    0    1                  18    5    1  8    13 


COMPOUND   SUBTRACTION.  41 1 

LONG  MEASURE. 

L.  M.fur.p,  yd  in, ft.  L.  M.fur.  p.  yd,  ft  in- 

(33.)  (5^    5   9   4   2    6     (34.)  9   1    7   18  5   1  11 

4  3    2   8   13    7  7  2   .5  19  1  2    9 


Aus.  123121  11  121   39  322 

35.  Two  men  travelling  the  same  road;  one  tnivels  at  the 
rate  of  27m.  2fur.  39p. ;  the  otlicr  at  the  rate  of  19m.  Ifur. 
17p.     At  night  how  fai- are  they  distant  ? 

Ans.  8m.  Ifur.  22p. 

LAND  OR  SQUARE  MEASURE. 
Ji.R.P,  ^JR.P,  Jl.R,P.  ^.R.P, 

(3G.)9G  2  16  (37.)  640  S  12  (38.)  96  0  18  (39.)  50  3  19 
87  3  18  114  4    3  74  2    4  13  1    5 


Ans.  8  2  38  525  3    9  21  2  14  37  2  14 

40.  A  father  dying  left  his  son  Joseph  200a.  2r.  20p 
and  to  James  180a,  3r.  39p.     What  is  the  diiference  il 
then- shares?  Ans.  19a.  2r.  2 If 

LIQUID  MEASURE. 

^al.  qt.  pt, 

i2     2     1  (42.)  1..     _       .     ^. 

3     2     14  ,3     0  96    2      8     2 


r.  Jilid.gal  qt.  pt,  T.    hJid.  gal  at. 

(41.)  8     2    42    2     1  (42.)  186    3      9     1 


Ans.  5     0     27     3     1  90     1      0 


^  4o.  A  person  bought  4hhd.  25gal.  of  cider:  — he  has 
smce  sold  2hhd.  15gal.  Sqt.  Ipt.     How  much  has  he  re 
"^'^;;^"^«-  Ans.  2hhd.  9gal.  Oqt.  Ipt. 

44    If  5hhd.  Igal.  Iqt.  Ipt.  of  oil  be  drawn  fiW6hhd. 
2giil  2qt.  Ipt.  how  much  will  remain  ? 

Ans.  Ihhd.  Igal.  Iqt.  Ojd, 

DRY  MEASURE. 

(450  44  2   1    1    (4C.)80   3   7   1,(47.)  789^0   5,  0 
32  3   2   1   ^      -^15   1    11      ■        

I   Ans.  11   2   7   0  {;5   2   6   0 

!  4'-^     ~"  — 


•42  COMPOUND    SUBTIIAOTIO.V. 

48.  From  TlOLu.  Ope.  5qt.  take  583bu.  2pc.  Gqt. 

Ans.  ISGbu.  Ope.  Tqt. 

49.  Kaieed  ISQbu.  Ipc.  Tqt.  Ipt.  of  corn;  have  siuce  sold 
167bu.  2pe.  Iqt, ;  whut  quantity  have  I  remaining  ? 

■AuH.  21bii.  8pc.  Gqt.  Ipt. 

,  TIME. 

K     M.  Y.    M.  hr.  min.  sec. 

(50.)  12     11      (51.)  7      1      (52.)  18    45     59 

7       5  8     10  2     51     28 


Ans.  5       G  8       3  15     54     31 

53.  .Subtract  1^5y.  9m.  from  450y.  llui. 

Ans.  325y.  2m. 

54.  Take  o6da.  141ir.  30min.  and  25,sec.  from  44da.  Ihr. 
48ni}n.  and  58sec.  Ans.  7da.  lliir.  18min.  33scc. 

•Vo/c.  The  intcn\Tl  or  «pace  of  lime  between  two  given 
i dates  is  thus  found:  Set  down  the  greater  date,  and  under  it 
the  less :  Begin  with  tlie  days.  If  the  upper  number  of  days 
be  greater  than  the  lower,  subtract  the  lower  from  it,  and  set 
down  the  remainder.  But  if  the  lower  number  be  gi*eater, 
add  as  many  days  to  the  upper  as  make  a  moiith  of  the 
lower,  and  subti'act  the  lower  therefrom;  then  carry  one  to 
I  the  months  of  the  less  date,  and  subtract  as  before,  and  so 
proceed.  ■'*^--     ■^*' 

EXAMPLES. 

55.  Abijah  was  born  on  the  15th  of  November,  1807, 
and  Josiah  on  the  IGth'of  July,  1811.     What  is  the  differ- 

'.  ence  in  their  asies  ? 


Y. 

M. 

de. 

1811 

T" 

IG 

1807 

11 

15 

An^.         3       8         1 

*NoTE.  —  July  is  the  seventh   month,  and   November  the 
eleventh. 

56.  Charles  was  born  on  the  18th  day  of  June,  1821. 
How  old  will  he  be  on  the  13th  day  of  August,  1840  ? 

Ans.  19y.  Im.  25da. 


»-»»i»MMw«iMiiMi»«M»MM«w»iiM«i»»»e»iMM»»^»ii«— — — Mi»»i»— «i»»  II I  il     ii    j»««— ——«—»— JMS  lirllriTii   T 

COMPOUND   DIVISION.  43 

57.  William  was  born  on  the  llth  day  of  August.,  1813, 
and  John  on  the  5th  day  of  July,  1827.  How  much  older 
is  William  than  John  ?  Ans.  13y.  10m.  25da. 

58.  A  man  gave  his  note  on  the  10th  day  of  May,  1824, 
and  lifted  it  on  the  8th  day  of  December,  1829.  For  what 
time  did  he  pay  interest  ?  Ana.  5y.  6m.  29da. 

API'LIOATION. 

59.  Bought  2  pair  of  stockings,  at  75  cts.  per  pair;  lOyds. 
of  linen,  at  87^  cts.  per  yard;  28yds.  of  domestic,  at  22  cts. 
jxjr  yard;  and  5  pair  of  gloves,  at  olj  cts.  per  pair;  and  to 
him  from  whom  I  bought  those  articles,  I  deliver  $50  00, 
out  of  which  he  is  to  t<akc  the  sum  due  him.  How  much 
change  will  there  be  coming  to  me?  Ans.  $26  771  cts. 

60^  If  I  buy  660yds.  of  muslin  for  $90  60  cts.,  and  sell 
the  same  again  for  $100  04  cts.,  how  much  do  I  gain  l)y 
the  sale  ?  Ans.  $9  44  cts. 

00.  Bought  50yds.  of  superfine  cloth  at  $8  75  cents  per 
yard;  30  pounds  of  coifee,  at  22 1  cts.  per  pound;  and  44 
bushels  of  salt,  at  $2  per  bushel.  What  sum  must  I  pay 
for  the  whole  ?  Ans.  $532  25  cts. 

62.  I  have  several  tracts  of  land ;  one  of  them  contains 
69Qa.  2r.  16p. ;  another  400a. ;  and  two  others,  each  63a.  3r. 
24p.     If  I  sell  200  acres,  what  number  remains  ? 

Ans.  1018a.  Ir.  24p. 

63.  Bought  400bu.  8pe.  of  wheat;  160bu.  of  rye;  150bu. 
2pe.  of  oats.  I  have  since  sold  225bu.  Ipe.  of  wheat;  37bu. 
2pe.  of  rye;  78bu.  3pe.  of  oats.  How  many  bushels  of 
each  have  I  remaining);'  C  175bu.  2pe.  wheat, 

Ans.      -j  r22bu.  2pe.  rye, 
(^    71bu.  Pj])e.  oats. 


COMPOUND  DIVISION. 

Compound  Divi^ion  teaches  to  divide  any  sum  or  quantity 
which  consists  of  several,  denominations. 

RULE. 

Begin  at  the  highest  denomination,  and  divide  the  several 
denominations  of  the  given  sum  or  quantity  one  after  ano- 


44  COMPOUND  DIVISION. 

tlier,  and  set  their  respective  quotients  underneath.  \Vlien 
a  remainder  occuig,  reduce  it  to  the  next  lower  denomina- 
tion by  multiplying  it  by  as  many  of  the  next  denomination 
as  make  one  of  that  denomination  from  which  the  remainder 
is  derived,  and  the  next  denomination  to.  the  product;  then 
divide  as  before,  and  so  proceed. 

JS'ote.  If  the  dividend  be  not  large  enough  to  contain 
the  divisor  reduce  it  till  it  ttjJI  be,  and  proceed  dfi  before. 

EXAMPLES. 

(1.)        %  cts.      (2.)      %    cts,m.      (3.)     %    ct^. 
2;12  61  3;187  91  4  4)168  99 

Ans.  6  30 J        Ans.  62  63  8         Ans.  42  24| 

6     cts.  8     cts. 

4.  Divide        366  18f    by  3      Ans.   122  06^ 

5.  496  75  8  62  09^  4- 

6.  384  87^  '  6  64  14j  + 

7.  587  681  9  65  29f  + 

8.  976  43f  11  88  76^  + 

9.  1979  BH        12  164  94i  + 

yd.  qp.  na.  yd,  qr,  na. 

10.  Divide      44    1    2   by  7      Ana.    6    11  + 

11.  56    3    3        11  5    0    2  + 

M.  fur.  P.  M.fur.  P. 

12.  Divide  105    5    22  by  12      Ans.  8    6    18  + 

13.  45    7    18  6  7    5      9  + 

hu.  pe.  qt  Jm*  pe.  qt.  pt. 

14.  Divide    48    2    0  by  4      Ans.  12    0    4    0 

15.  ■    86    3    7        3  28    3    7    1  + 

JYote.  "When  the  divisor  is  more  than  12,  work  by  Long 
Division.  Divide  the  highest  denomination  of  the  given 
sum  by  the  divisor,  and  reduce  the  remainder,  if  any,  to  the 
next  lower  denomination,  adding  to  it  when  reduced  the 


COMPOUND  DIVISION.  45 

number  there  is  of  that  denomintition  in  the  given  sum  or 
quantity.     Then  divide  as  before,  and  so  proceed. 

EXAMPLES.  , 

$  cts.m.  $    cis. 

^16.)  Divide  88  45  6  by  19.     ( 17.)  Divide  250  50  by  25. 
'ii'OT-  $  cts.m.  $  cis, 

19)88  45  6.    (Ans.4  65  5.    '25)250  50.   (Ans.  10  02. 

7G  25 


.124  0  50 

114  50 


105  00 

95 

100 
95 

11  Kcmainder. 

$  els.    m.  $  ets. 


m. 


18.  Divide  98  77  8  by  44    Anj?.  2  24  4  + 

19.  45  66  5  .36  1  26  8-f 

20.  77  87  5  96  0  81  1-f 

21.  288  68f  0  108  2  67j  + 

22.  496  37|  0  132  3  76  0-f 

23.  47  68  7  45  1  05  9  + 

24.  196  75  0  78  2  62  2  + 

25.  496  87^  0  97  6  12  2-f 

26.  376  81 J  0  123  3  06  3  + 

27.  A  laborer  received  for  thirty  days  $900.     How  much 
did  he  receive  per  day  ?  "Ans.  $30. 

28.  If  a  boy  receive  $60  for  twelve  months  work,  how 
much  is  that  for  cue  month  ?  Ans.  $5. 

29.  How  many  bushels  of  com  may  be  bought  for  ^00, 
at  $2  per  bushel  ?  Ans.  200  bushels. 

30.  When  72  bushels  of  com  cost  $56  25  cents,  what 
is  the  price  of  one  bushel  ?  Ans.  78cts.  Im.  -f- 

31.  Suppose   S1875   81  i   cents   to   be  equally  divided 
among  125  men,  what  will  be  the  share  of  each  man  ? 

Ans.  S15  OOi  cent,  -f 


46  llEDUCTION   DESCENDING 

32.  89  men  agree  to  equally  divide  ISOgals.  2qts.  Ipt.  of 
brandy  among  them,  how  much  will  be  the  share  of  each  ? 

Ans.  Igal.  2qt.  Ipt. +  48. 


REDUCTION  DESCENDING. 

if 

Reduction  Descending  teaches  to  change  any  sum  or  quan- 
tity to  a  lower  denomination,  but  retaining  the  same  value. 

RULE, 

Multiply  the  highest  denomination  of  the  given  sum  o^ 
quantity  by  as  many  of  the  next  lower  denomination  as 
make  one  of  the  higher,  adding  to  the  product  the  number 
there  is  of  that  denomination  in  the  given  sum  or  quantity. 

J^ote,  To  reduce  dollars  to  cents,  annex  two  ciphers  to 
the  dollars. 

EXAMPLES. 

FEDERAL  MONEY. 

( 1.)  Reduce  $18  50  cts.  to  cts.      (  2.)  Bring  $75  to  ets. 
100  100 

Ans.  1850  7500 

3.  Bring  $100  to  cents.  Ans.  10000  cents. 

4.  Reduce  20  dollars  to  cents.  Ans.  2000  cents. 
6.  Bring  25  dollars  to  cents.  Ans.  2500  cents. 
6.  Reduce  45  dollars  to  cents.  Ans.  4500  cents. 
J^ote.  To  reduce  dollars  to  halves,  quarters  or  thirds  of 

a  cent,  bring  them  first  into  cents,  and  then  bring  the  cents 
into  halves,  quarters  or  thirds,  as  required. 
(7.)  Bring  $50  into  half  cts.  (  8.)  Bring  $40  into  thirds  of  a  ct. 
100  100 


5000  4000 

2  3 


Ans.  10000  halves.  Ans.  12000  thirds. 

(9.)  Reduce  25  cts.  to fourtha.  ( 10.)  Reduce  12  cts.  to  thh-ds. 
4  3 

Ans.   100  fourths.  Ans.  36  thirds. 

11.  Reduce  10  dollars  to  dimes.      Ans.  100  dimes. 


REDUCTION  DESCE:<DINa.  47 

12.  Reduce  220  dollars  to  mills.       Ans.  220^000  mills. 

13.  Reduce  $426  88  J  cts.  to  halves  of  a  cent. 

Ans.  85377  halves. 

14.  Bring  §487  44|  cents  to  fourths  of  a  cent. 

A^s,  194979  fourths. 

15.  Bring  $17  18 1  cents  to  fourths  of  a  cent. 

Ans.  6875  fourths. 

AVOIRDUPOIS  WEIGHT. 

10.  Bring  2  tons  to  cwt.  (  17.)  Reduce  260  cwt  to  quarters. 
20  4 

Ans.  40  cwt.  Ans.  1040  quarters. 

18.  Reduce  36qr.  to  pounds.  Ans.  10081b. 

19.  Bring  17  pounds  to  ounces.  Ans.  272oz. 

20.  Bi-iug  2qr.  251b.  lOoz.  to  drams.         Ans.  20896dr. 

TROY  WEIGHT. 

21.  Reduce  20  penuyweidits  to  trains. 
.  24 

80 
40 

Ans.  480  grains. 

22.  Reduce  5  ounces  to  grains.  Ans.  2400gr. 

23.  Bring  40  pounds  to  peimyweights.      Ana.  9600dwt. 

24.  IIow  many  grains  are  there  in  191b.  lloz.  14dwt. 
-Igr-  Ans.  115077gr. 

ArOTHECARlES^  WEIGHT. 

25.  Reduce  40  pounds  to  ounces.  Ans.  480oz. 

12 

480 

26.  Bring  72oz.  to  drains.  Ans.  576dr. 

27.  Reduce  151b.  9oz.  4dr.  2sc.  17gr.  to  grains. 

Ans.  91017gr. 
LONG  MEASURE. 

28.  Reduce  10ft.  to  inches.  Ans.  120in. 

]2 

120 


148  REDUCTION  BESOENDIKG. 

29.  Bring  40yd.  to  feet.  Ans.  120ft. 

30.  Reduce  120yd.  1ft.  4in.  to  mctcfl.     Ans.  4336m. 

81.  Reduce  20  miles  to  yards.  Ans.  85200yd. 

82.  Reduce  450m.  6fur.  32p.  to  poles.     Ans.  144272p. 

83.  In  2L.  Im.  3fur.  16p.  3yd.  2ft.  lOin.  Kow  many 
inches?  Ans.  470590in. 

CLOTH  MEASURE. 

34.  Reduce  22  quarters  to  xiails.  Ans.  88na. 

4 

88 

35.  Bring  86yd.  to  qr.  Ans.  l'44qr« 

36.  Bring  20  English  Ells  to  qHarters.  Ans.  lOOqr 

37.  Bring  20  French  Ells  to  quarters.  Ans.  120qr. 

38.  Bring  8yd.  Iqr.  to  qr.  Ans.  83qr. 

39.  In  iSyd.  2qr.  Ina.  how  many  nails?  Ans.  S13na. 

LAND  OR  SQUARE  MEASURE. 

40.  Bring  2  roods  to  perches.  ♦     Ans.  80  pei'ches. 

40 

80 

41.  Reduce  140  acres  to  perches.     Ans.  22400  perches. 

42.  Bring  54  acres,  3  roods,  23  polcvS,  to  poles. 

Ans.  8783p. 

43.  Bring  6  squ/ire  feet  to  square  inches.      Ana.  864iu. 

44.  Bring  120  square  yards  to  square  inches. 

Y'  ^  Ans.  165520in. 

45.  Bring  29  square  yards,  2  square  feet,  102  square 
inches  to  square  inches.  Ans.  37974  square  inches. 

LIQUID  MEASURE. 

46.  Reduce  31  quarts  to  pints.  Ans.  62p4. 

2 

.62 

47.  Bring  28  gjil.  to  quarts.  Ans.  112qt. 

48.  Reduce  5bhd.  to  gallons.  Ans.  315gal. 

49.  In  6  tons,  how  many  pints  ?  Ans.  12096pt. 

50.  Reduce  4hhd.  3qt.  to  pints.  Ans.  2022pt. 

51.  Bring  5  tons.  Ihhd.  15gal.  Iqt.  Ipt.  to  pints. 

Ans.  10707j)t.  | 


ff 


HHWHU«W—»W»— lt«<MI— 


REDUCTION   ASCENDING. 

DRY  MEASURE. 
52.  Reduce  IGqt.  to  pints. 

82 

53  ]?ring  32pe.  to  quarts.  * 

54.  Reduce  7bu  tc  pecks. 

55.  Reduce  12bu.  to  pints. 

56.  Bring  24bu.  Ipe.  2qt.  Ipt.  k>  pints. 

TIME. 

57.  Bring  40  minutes  to  seconds. 

60 


49 


Ans.  32pts. 


Ans.  256qt. 

Afts.  28pe. 
Ans.  768pts. 
Ans.  1557pt. 


Ans.  2400860. 


58. 
59. 
60. 


2400 

Bring  20  hours  to  seconds.  Ans.  72000sec 

Reduce  12  years  to  months.  Ans.  144m. 

Bring  45  years  to  days.  Ans.  16425da. 

61.  Reduce  3  days,  5hr.  29nnn.  to  minutes. 

Ang.  4649min 

62.  Reduce  7y.  3w.  4da.  20hv.  20min.  and  20sec.  to 
seconds.  ^ Ans.  222380420sec 

t 
REDUCTION  ASCENDING. 

Reduction  Ascending  teaches  to  change  any  sum  or  quan- 
tity to  a  higher  denomination. 

EULE. 

Divide  the  given  sum  or  quantity  in  the  lowest  denomi- 
nation, by  as  many  of  that  denomination  as  make  one  of  the 
next  highor,  and  so  on,  until  you  have  brought  it  into  that 
denomination  which  your  question  requires. 

jyote.  Mills  may  be  brought  to  dollars,  cents  and  mills, 
by  cutting  off  one  figure  on  the  right  for  mills,  two  more 
for  cents;  the  rest  will  be  dollars.  Or  to  bring  cents  to 
dollai*s  and  cent,s,  cut  off  two  figures  on  the  right  for  cents. 

EXAMPLES. 


FEDERAL  MONEY. 

1.  Bring  2800  cents  to  dollars. 
28100 


Ans.  $28. 


^  }dO  REDUCTlOiJJ    ASCENDINQ. 

2.  Ering  xl'2il2  mills  to  dollars,  cents  and  mills. 
11112-212  Alls,  m  2iiets.  2m. 

3.  Bring  4-144  cents  to  dollars  and  CQjits. 

Ans.  $44  44cts. 

4.  Bring  864  halves  of  a  cent  to  whole  cents. 

Aus.  432cts. 

5.  In^063  thirds  how  many  cents  ?  Ans.*321cts. 

6.  In  501  fourths  hnv  many  cent^?         Aus.  147icts. 

7.  Brh)g  680  thii'ds  to  cents.  xVns;  21-Octs. 

AVOIBDUPQIS  WEIGHT. 

8.  Bring  IlSib.  to  quarters. 
28)ll«(An9.  4<ir.  61b. 

112  .; 

6 

9.  Bring  90qr.  to  cwt.  Ans.  22e^?t.  2qr. 

10.  Bring  17811b.  to.cM^t.  Aus.  i5cwt.  3qr.  171b. 

11.  In  I872dr.  how  many  pounds?  Ans.  71b.  5oz.  • 

12.  Bring  75cwt.  to  tons.  Ans.  3t.  15cwt. 

13.  Bring  98561b.  to  cwt.  Aus.  88cwt. 

TEOY  WEIGHT. 

14.  Bring  186oz.  to  pounds.  Ans.  15Ib.  6oz: 
12)186    ■  : 

15Ib.  6oz. 

15.  In  544dwt.  how  many  pounds  ?  Ans.  2Ib.  3oz.  4dwt. 

16.  Bring  960dwt.  to  pounds.  Ans.  41b. 

17.  Bring  9624gr.  to  pounds.  Ans.  lib.  8oz.  Idwt. 

APOTIIEOABIES^  WKimiT. 

18.  Bring  2105  to  RmiplcP.  Ans.  129. 
2tO)24IO 

12 

19.  Bring  27209  to  ounccfi.  Ans.  113 3  23  2 d. 

20.  Bring  126(p0gi-.  to  pounds.  Ans,  2fe  23  33. 

21.  In  155520gr.  how  niany  pounds  ?  A»av27-,|b, 

LONG  MEASURE.  '^ ] 


f, 


22.  Brine;  120  miles  to  leas^Q9,.  Ans.  40^ 

3)120  ' 

40 


REDUCTION   ASCENDING.  51  j 

23.  Bring  1280  poles  to  fur.  Ans.  32fui'. 

24.  Bring  2880  poles  to  leagues.  Ans.  31. 

25.  Bring  5760  poles  to  leagues.  Ans.  61. 

CLOTH  MEASURE. 

26.  In  60  quarters  how  many  yards  ?  Ans.  15yds 

4)60 

15 

27.  Bring  4000  nails  to  yards.  Ans.  250yds. 

28.  Bring  1260  quarters  to  E.  F.  Ans.  210  E.  F. 

29.  Bring  1818  nails  to  yards.     Ans.  113yds.  2qr.  2na. 

'  LAND  OR  SQUARE  MEASURE. 

30.  In  2400  perches  how  many  Roods  ?         Aug,  60  R. 

410)240|0 
— * 

60 

31.  Bring  2040  perches  to  Acres.  Ans.  12A.  311. 

32.  Bring  1908020  perches  to  A.  Ans.ll925A.  OR.  20P. 

33.  In  1728  square  inches  how  many  square  feet  ? 

Ans.  12  feet. 

LIQUID  MEASURE. 

34.  In  480  gills  how  many  pints  ?  Ans.  120  pis 
4)480  ^ 

120 

85.  Bring  1840  pts.  to  gals.  Ans.  230  gals. 

36.  Bring  1890  gal.  to  hhdn.  Ans.  30  hhds. 

37.  In  504  gallons  how  many  bar.  ?  Ana.  16  bar. 

DRY  MEASURE. 

38.  In  800  pint;3  how  many  qts  ?  Ana  400  ats 
2)800  *   ■ 

400 

39.  Bring  240  pints  to  pe.  Ans.  15  pe. 

40.  Bnng  8888  pecks  to  bn.  .         Ans.  2222  bu. 
41-  In  12840  pints  how  many  bu.  ?  Ans.  2G0bu.  2pe.  4qt! 


^62  IIEDUOTION    ABCBNDINO. 

TIME. 

42.  Bring  2400  seconds  to  minutes.  Ans.  40  miu 
r)|0)240j0  |[ 

40 

43.  In  7200  seconds  how  many  hours  ?       Ans.  2  lioiirs. 

44.  Bring  144  months  to  years.  Ans.  T  2  years. 

45.  In  4649  minutes  how  many  days? 

Ans.  3da.  5hr.  29m. 

PROMISCUOUS   EXAMPLES. 

1.  In  20  dollars  how  many  cents  ?        Ans.  20Q0  cents. 

2.  In  63  roods  how  many  perches?    '    "Ans.  2520  per. 

3.  How  many  miles  are  there  in  98  fur.  ?  Ans.  12m.  2fur. 

4.  In  175  pecks  how  many  bushels?     Ans.  4obu.  oj^c. 

5.  How  many  min.  are  theje  in  720  sec.  ?  Ans.  12miii. 

6.  In  103  pints  how  many  quarts  ?        Aus.  51qts.  Ipt. 

7.  In  1824  cents  how  many  dollars  ?     Ans.  $18  24  cts. 

8.  In  8t.  15cwt.  how  many  hundred  weight  ? 

Ans.  175  cwt. 

9.  How  many  English  Ells  arc  there  in  one  hundred 
quarters  of  a  yard  ?  Ans.  20  E.  Ells. 

10.  How  many  scruples  are  there  in  9  3  ?       Ans.  27  9. 

11.  In  203  days  how  many  weeks?  Ans.  29w. 

12.  In  lOSdwt.  how  many  ounces?  Ans.  5oz.  8d\Yt. 

13.  How  many  cwt.  are  there  in  20  tons  ?     Ans.  400cwt. 

1 4.  In  202  cents  how  many  qrs.  of  a  cent  ?    Ans.  808qrs. 

15.  How  many  dollai-s  are  there  in  8762  cents  ? 

Ans.  $87  62cts. 

10.  How.many  fur.  are  there  in  3m.  Ifur.  ?  •  Ans.  25fur. 

17.  In  i31b.  avoirdupois  how  many  drams  ?  Ans.  3328dr. 

18.  In  21  gallons  3qts.  Ipt.  how  many  pints? 

Ans.  175  pints. 

19.  How  many  Ells  F.  are  there  in  60  qrs.  ?  Ans.  lOE.F. 

20.  How  many  lbs.  are  there  in  2461  dwt. 

Ans.  101b.  3oz.  Idwt. 

21.  How  many  drams  are  there  in  7251b.  6oz.  av.  ? 

Ans.  185696dr. 

22.  In  12yds.  2qrs.  Ina.  how  many  nails  ?     Ans.  201na. 

23.  How  many  cwt.  are  there  in  275521b.  ?  Ans.  246cwt. 


RULE   OF   TWO.  Oo 

RULl^:  OF  TWO. 

The  Rule  6f  Two  is  that  iii  wMcli  two  terms  are  given 
to  find  «i,  tliivd,  which  is  the  answer. 

To  Ihul  the  whole  cost  of  any  number  of  articles  at  any 
price  per  article. 

RULE. 

Multiply  the  articles  by  the  given  price  of  one  article; 
the  product  will  I'e  the  annwer. 

EXAMPLES. 

1.  What  will  eleven  oranges  come  to  at  12 i  cente  each? 

2.  How  much  will  60  bushels  of  apples  come  to  at  8 i 
cents  per  bushel  ? 

11  00 

12^  the  given  pr.  of  one  article.  8 1 

132  *  480 

.       S^the  half  of  11  is  5i         15  the  fourth  of60  is  16 


Ans.  ^1  37i  .  Ans.  U  95 

o.  ITow  much  will  105  pounds  of  sugar  come  to  at  12  J 
cts.  per  pound  ?  "  Ans.  $13  12^  cent«. 

4.  Whi)t  will  60  apples  come  to  at  2^  cents  each  ? 

Ans.  ^1  35  cents. 

5.  "What  will  87^'  pounds  of  beef  come  to  at  tlfree  cents 
per  pound?  Ans.  $2  G2^  cents. 

0.  IJought  40  pounds  of  coffee  ai;  81}  cents  per  pound; 
what  did  it  amount  to  ?  Ans.  $12  50  cts. 

7.  IVirchascd  ninety  gallons  of  molasses  at  55  J  cents  per 
g;i1km  ;  what  did  it  amount  to?  Ans.  $50  02 1  cts. 

8..  What  will  nineteen  pounds  of  biwion  come  to  at  8J 
cents  per  pound  ?  •      Ans.  $1  58  J  cents. 

9>  Wliat  is  tlic  -cost  of  400  poumls  of  cheese  at  8^  cents 
jper  pound?  Ans.  -SSo  33}  cents. 

10.  ]>ought  101  buslicls  of  wheat  at  ^1  04  cents  per 
bushel;  wh;ii  did  it  amount  to?  Ans.  -$105  04  cents. 

11.  What  will  022"  gallons  of  whiskey  come  to  at  02^ 
•  jcentii  per  gallon?  Ans.  $39  OG^  cents. 

J  2.  What  \Yill  25  bushels  of  oats  come  to  at  25  cents  per 
'Ijushel?  Ans.  $0  25  cents 


fi  * 


MatWHaniiaMinpi 


54  UUXE   OF  TWO; 

13.  How  mucli  will  eleven  pounds  of  butter  come  to  ut 
8^  cents  per  pound?  Any.  91  j  cents. 

14v.  What  will  84  pounel»  of  "lard  come  tn)  at  ten  cents 
per  pound  ?  Ans.  $8  40  cents. 

15.  How  inuch  will  two  thousand  books  come  to  at  20 
cents  per  book  ?  Ans.  $400.  [ 

16.  What  cofc^t  789  pound.s  of  iron  at  4 1  cents  per  pound? 

Ans.  ^35  50^  cents. 

17.  What  cost  40  bushels  of  rye,  at  20  cts.  per  bushel  ? 

Ans.  8«. 

18.  What  will  6  pounds  of  soap  come  to  at  ten  cents  per 
•j>ound  ?  Ans.  60  cents. 

■When  iti.«>  rcquh'ed  to  know  how  many  articles  may  be 
bought  with  any  sum  of  money. 

llUlJfl. 

i)i^■ide  the  sum  by  the  price  of  one  article;  have  the 
lividond  and  divisor  of  one  dfcuumination.  The  quotient 
will  be  the  number  of  articles. 

EXAMPLKS. 

1.  How  many,  pounds  of  butter  may  be  bought  with  ^1  60 
ccntS;  at  8  cents  per  pound  ? 

2.  How  many  pounds  of  iron  can  I  buy  with  $7  00  cts. 
at  3^  cents  per  pound  ? 


8)1  60 
Aus.     20  lbs. 

hiilves. 

3^    7  00 

2           2 

T)  14  00  halves 

Ans.  200  pounds. 

3.  When  one  prmnd  of  sugar  costs  12  i  cents,  how  many 
pounds  may  be  had  for  30  dollars?  Ans.  240  pounds. 

4.  A  gentleman  gavd"  his  son  60  dollars,  which  he  was  to 
lay  out  for  tea  at  37^  cents  per  pound.  How  many  pounds 
did  he  buy?  Ans.  160  pounds. 

5.  How  many  bushels  of  corn  can  I  buy  for  400  dollars^ 
if  I  give  13  cents  per  bushel  ? 

Ans.  3076bu.  3pe.  5qt.  Ipt.  + 

6.  When  I  can  buy  one  pound  of  tobacco  for  25  cents, 
i  how  many  pounds  can  I  buy  for  $75  ?       Ans.  300  pounds. 


RULE   OF   TWO.  00 

7.  How  many  pounds  of  iron  may  be  bought  with  37 
dollars,  at  4  cents  per  pound  ?  Aus.  925  pounds. 

8.  Having  ^378  10  cents,  a;id  wishing  to  purchase 
feathers,  what  quantity  can  1  purchase  at  83^  cents  per 
pound?  Ans.  1134^- pound. + 

9.  If  sixty  dollars  be  the  price  of  an  acre  of  land,  how 
many  acres  can  I  have  for  $192  GO  cent^? 

Ans.  3^1.  Or.  33p.-f 

10.  Suppose  a  man  lias  ^1900  06  J  cents,  and  is  desirous 
to  purchase  salt.  IIow  many  bushels  can  he  buy,  at  1  dol- 
lar 62}  cents  ?  *        Ans.  1160^  bu.+ 

n .  How  many  pounds  of  cofl'ec,  at  22  cents  per  })ound, 

can  I  have  for  22  dollars  ?  Ans.  100  pounds. 

•  12.  How  many  pounds  of  pork,  at  three  cents  per  pound, 

can  I  have  for  960  dollars  60. cents?     Ans.  32020  pounds. 

lo.  How  many  yards  of  cloth,  at  15  cents  per  yard,  can  I 
have  for  450  dollars  45  cts.  ?  Ans.  3003  yards. 

14.  How,  many  fowls,  at  6}  cents  each,  can  I  buy  for 
ninety  dollars  ?  *  Ans.  1440  foTvls. 

When  a  number  of  articles  cost  any  sum  of  money,  o.nd 
the  price  of  one  article  is  required  at  the  same  rate. 

RULE. 

Divjde  the  w'hole  cost  by  the  number  of  articles ;  tlio 
quotient  will  be  price  of  one  article. 

Note.  If  the  dividend  be  not  large  enough  to  contain  the 
divisor,  reduce  it  till  it  will  be. 

EXAMPLES. 

1.  If  100  bushels  of  corn  cost  12  dollars  50  cents,  wh?.t| 
is  the  price  of  one  bushel  at  the  same  rate  ?  | 

2.  If  4.}  pounds  of  pepper  cost  $2  00  cents,  what  cost' 
one  pound  at  the  same  rate  ? 

The  axtidt^.  lOia    12  510        4^     2  00 

~ 2*  2 

^ng.  12  J  cts. 1 

9)    4  00 
•  Ans.  44  cts.  4.m.  -f 


56  RULE   OF   THREE. 

3.  If  S  fish  cofit  50  ote.,  what  will  one  cost? 

Ans.  84-  cents. 

4.  If  I  buy  40  bushels  of  flaxseed  for  40  dollars  40  cents, 
how  much  do  I  give  per  bushelj  Ans.  ^1  01  cent. 

5.  A  man  travelled  420  miles  in  twelve  days.     How  far 
did  he  travel  each  day  ?  Ans.  85  mi^es. 

0.  Bought  120  pair  of  shoes  for  400  dollars  60  cents. 
What  was  the  cost  of  one  pair?  .       Ans.  83  33 1  qU. 

7.  Bought  6000  gallons  of  whiskey  for  nine  hundred 
dollai-s.     What  was  the  price  of  one  gallon  ? 

Ans.  15  cents. 

8.  If  I  buy  1517^  acres  of  land  for  7500  dollars  37j 
cents,  how  much  does  it  cost  me  per  acre  ? 

Ans.  U  94  J  cts.  + 

9.  A  merchant  bought  1950  penknives  for  960  dollars 
44^  cents.     What  did  one  cost?  Ans.  49 i-  cts. -f 

10.  If  I  buy  22  ^  yards  of  cloth  with  7  dollars  50  cents, 
what  cost  one  yard?  Ans.  33 J  cents. 

11.  I  was  offered  2000  books  for  $500  00  cent.^.     Tell 
me  what  one  book  would  cost  at  that  rate  ?     Ans.  25  cents. 

12.  I  was  offered  2000  books  for  ^380  50  cents.     How 
much  was  that  for  one  book  ?  Ans.  19  cents.  -|- 

13.  When  a  man's  yearly  income  is  $474  50  cents,  how 
much  is  it  per  day  ?  Ans.  $1  30  cents. 

14.  If  seven  months^  work   bring  $25  00  cents,  how 
much  will  one  month  bring  ?  Ans.  $3  57  cents.  + 

15.  Suppose  tlie  President  of  the  United  States  receive 
$25000  00  cents  a  year,  how  much  is  that  per  day  ? 

Ans.  $68  49  cts.  3m. -f 


PROPORTION;  OR,  RULE  OF  THREE. 

The  Rule  of  Three  is  that  in  which  three  terms  are  given 
to  find  a  fourth  or  answer. 

RULE. 

Set  that  term  in  the  third  place  which  is  the  same  kind 
of  the  answer.  Consider  from  the  nature  of  the  question 
whether  the  answer  ought  to  be  greater  or  less  than  this 
third  term.  If  it  is  to  be  greater,  set  the  greater  of  the  two 
remaining  terms  in  the  middle  for  the  second,  and  the  less 
for  the  first ;  but  if  it  is  to  be  less,  set  the  le«s  of  those  two 


RULE   OP   THREE.  57 

teriiis  ill  the  middle  for  the  second  term,  and  the  otlier  for 
the  first.  Then  have  the  first  and  second  terms  of  one  de- 
nomination. If  the  third  term  consist  of  several  denomi- 
nations, reduce  it  to  the  lowest  deubmination  in  it;  then 
multiply  the  second  and  third  terms  together,  and  divide 
the  product  hy  the  fir>t  term.  The  answer  will  ]>e  of  the 
same  dcQominatiou  as  the  third  ternj. 

A'^oie.  The  operation  may  frequently  be  performed,  thus: 
If  the  first  term  will  divide  the  second  by  the  quotient,  mul- 
tiply the  third;  or  if  the  second  will  divide  the  first  by  the 
quotient^  divide  the  third  term. 

EXAMPLES. 

1 .  If  four  bushels  of  cora  cost  80  cent*';  how  much  will 
S  bush(!lrf  cost  ? 

2.  If  three  yards  of  cloth  costi  fifty  cents,  how  much  will 

ten  yards  cost  y 

hu.       lu.         cts.  yd.        yd.  cts. 

4     :     8  :     :  80  3     :     10  :'    :  50 


o 


10 


Aus.  $1  GO  3  1  500 


Ans.  ^1  66f 

3.  If  four  yards  of  muslin  cost  six  cents,  what  will  eight 
cost?        ^  Ans.  12  cents. 

4.  If  six  yards  of  cloth  cost  IT  cents,  what  Avill  seven 
yards  come  to  at  the  same  rate'/  Ans.  19  cents  8m.  + 

5.  If  five  bushels  of  potatoes  cost  80  cents;  what  cost  14 
bushels  at  the  same  rate?  Ans.  ?>2.24  cents. 

6.  If  four  bushels  of  corn  cost  $2  00  cents,  how  much 
wU  12  bushels  cost  at  the  same  rate?       Ans.  ^6  00  cents. 

7.  If  eight  yai-ds  of  silk  cost  40  cents,  how  nmch  will  16 1 
yards  cost  ?  Ans.  80  cents.  I 

8.  If  three  pounds  of  cheese  cost  10  cents,  what  will  80 
pounds  come  to  at  the  same  rate?  Ans.  ^2  66 f  cents. 

9.  If  six  pounds  of  coftee  cost  55  cents,  what  will  75 
•pounds  come  to  at  the  same  rate  ?  *     Ajis.  $6  87j  cts. 

10.  If  2^  bushels  of  salt  cost  U  08  cents,  how  much 
will  15 i  busbals  come  to  at  the  same  rate  ? 

Ans.  $24  88  J  cents. 


58  RULE   OF   THREE. 

11.  Boiiglit  24  po-nnds  of  beef  for  $1  62^  cents,  how 
much  is  90^  pounds  worth  at  that  rate  ? 

Ans.  16  12|  cents.  -^ 

12.  "What  arc  60  bushels  of  apples  worth,  when  13 
bushels  cost  45  cents  'f  Ans.  2  dollars  07^  cents.  4- 

lo.  If  8  bushels  of  potatoes  cost  3  dollars  94  cents,  what 
will  105  bushels  cost?  Ans.  51  dollars  71i  cents. 

14.  If  45  cents  buy  11  pounds  of  tobacco,  how  much  will 
91 1  cents  buy  at  that  rate  ?  Ans.  22ilb.  + 

15.  What  will  22  books  come  to,  if  60  cost  20  dollars  51 
cents?  •  Ans.  7  dollars  52  cents.  + 

16.  If  1  yard  2  quarters  of  cloth  cost  56^  cents,  what  will 
17  yards  1  quarter  cost?  Ans.  6  dollars  46f  cts.-+ 

17.  If  4  dollars  will  pay  for  16  days'  work,  how  many 
days  work  may  be  had  for  98  dollars  ?  Ans.  392  days. 

18.  If  2  J  bushels  of  salt  cost  2  dollars  62 fr  cents,  how 
many  bushels  may  be  had  for  556  dollars  18|-  cents  ? 

Ans.  529  f  bushels.  + 

19.  If  7  pounds  of  coffee  cost  87*  cents,  what  must  I  pay 
for  244  pounds  ?  "  Ans.  30  dollars  50  ct>\ 

20.  If  450  barrels  of  flour  cost  1350  dollars,  what  will  8 
barrels  cost  ?  Ans.  24  dollars . 

21.  If  750  men  require  2250D  rations  of  bread  for  .a 
month,  what  will  a  garrison  of  1200  require  ? 

Ans.  36000  rations. 

22.  If  12  men  can  do  a  piece  of  work  in  20  days,  in  what 
time  will  18  men  do  it?  Ans.  13 J  days. 

23.  Wliat  will  be  the  cost  of  17  tons  of  lead,  if  5  tons 
cost  500  dollars?  Ans.  1700  dollars. 

24.  If  a  pasture  be  sufficient  for  3000  horses  18  days, 
how  long  will  it  be  sufficient  for  2000  ?  Ans.  27  days. 

25.  ]f  8  men  can  build  a  tower  in  12  days,  in  what  time 
can  12  do  it  ?  Ans.  8  day*. 

26.  IIow  much  carpeting  that  is  1^  yards  in  breadth, 
will  cover  a  lioor  that  is  7^  yards  in  length,  and  5  yards  in 
breadth  ?  Ans.  25  yards. 

27.  How  many  yards  of  matting,  2^  feet  ])road,  will  cover 
a  floor  that  is  27'feet  long  and  20  tbet  broad?    Ans.  72yds. 

28.  What  must  %e  the  length  of  a  board  that  is  9  inches 
in  width,  to  make  a  surfixce  of  144  inches  or  a  square  foot  ? 

Ans.  16  inches. 

29.  If  5  yard;?  of  cloth  cost  1  dollar  12  J  cents,  what  is 


RULE   OF   TUllEE.  59, 


the  value  of  -1  pieces,  each  containing  8  yards  and  1  quar- 
ter ?  Aus.  7  dollars  42^  cents. 

30.  If  IJ  ounces  of  spice  cost  13  cents,  what  cost  16^ 
ounces?  Ans.  1  dollar  40 1  cents.  + 

31.  If  100  "skeins  of  silk  cost  25  dollars  21  cents^  how 
many  may  be  bought  for  1800  dollars  50  cents  ? 

Ans.  7142  skeins.  + 
82.  If  2  dollars  50  cents  pay  fgr  two  weeks'  boaiwiing, 
how  long  can  I  board  for  40  dollars  40  cents ! 

Ans.  32  weeks  2  days.  + 

33.  Suppose  A  hired  to  B  12  months  for  60  dollai-s,  after 
Avorking  7  months  B  agreed  to  pay  A  at  that  rate,  what  must 
he  pay  '{  Ans.  35  dollars. 

34.  If  1  cwt.  of  sugar  cost  11  dollars  37^  cents,  what  will 
IScwt.  3qv.  191b.  cost?         Ans,  215  dollars  21  cts.  -f  10^ 

35.  How  many  men  will  it  require  to  repair  a  piece  of 
work  in  50  days,  when  14  men  can  do  it  in  100  days  ? 

Ans.  28  men. 

36.  Li  what  time  will  600  dollars  gain  the  interest  which 
80  dollars  would  gain  in  15  years  ?        _  Ans.  2  3'cars. 

37.  If  2  yards  of  tape  cost  50  cents,  what  will  54  j^nglish 
Ells  3qr.  cost  at  the  same  rate?         Ans.  17  dollars  6f  cts. 

38.  If  the  price  of  1  acre  of  land  be  5  dollars  25  cents, 
what  will  350  acres  1  rood  18  perches  come  to  at  that  rate? 

Ans.  1839  dollars  40  cts.  3ui.  4-  \ 

JWUe.  In  all  cases  wherein  labor  is  required  to  be  per- 
formed, the  day  must  be  reckoned  at  12  hours. 

39.  Suppose  20  days  be  required  for  12  men  to  build  a 
liousc,  in  what  tin:ic  can  18  men  do  the  same  ? 

Aus.  loda.  4hr. 

40.  In  what  time 'will  48  men  make  a  fence  which  12 
men  can  do  in  24  days  ?  Ans.  6da. 

41.  If  G  men.  can  do  a  piece  of  work  in  18  days,  hOw 
long  will  it  require  12  men  to  do  it  ?  Ans.  9da. 

42.  If  8  men  can  mow  a  piei-e  of  meadow  in  24  da3'S, 
how  many  men  can  do  it  in  1  days  ?  Ant.  48  men. 

43.  If  a  traveUcv  jx^rform  a  journey  in  5  days,  when  the 
days  are  11  hours  long,  how  lono;  will  ho  require  to  do  it 
when  tlio  days  ar«  16  hours  long?  Ans.  3da.  8hr. 

44.  How  many  yaxda  of  paper  2^   feet  wide  will  be 


j60  RULE   OF   THREE 


required  to  ooTer  a  wall  which  is  12  feet  long  and  9  feet 
high  ?  Ans.  14yd.  1ft.  2in.  + 

45.  What  quantity  of  linen  that  is  3  quarters  of  a  yard 
wide,  will  line  7 J  yards  of  cloth  that  is  lA  jards  wide? 

Ans.  15  yards. 

46.  A  ship's  crew  consisting  of  45  men  are  provided  with 
4500  pounds  of  bread,  of  which  each  man  eats  one  pound 
pcr-^ay ;  how  many  weeks  will  it  last  them  ? 

Ans.  14w.  2 da. 

PROMISCUOUS   EXAMPLES, 

IN  THE  RULE  OF  TWO  AND  THREE. 

47.  If  7  oxen  be  worth  10  cows,  how  many  cows  will  21 
oxen  be  worth  ?  Ans.  80  cows. 

48.  If  boai-d  for  one  year  amount  to  182  dollars,  what 
will  39  weeks  come  to  ?  Ans.  $13(>  50  cts, 

49.  If  30  bushels  of  rye  be  bought  for  120  bushels  of 
1  potatoes,  how  many  bushels  of  rye  can  be  bought  for  COO 
! bushels  of  potatoes?  Ans.  }50bu.  rye. 

60.  A  f\irmcr  made  14G  barrels  of  eider,  which  he  after- 
wards sold  at  3  dollars  12 1  cents  a  barrel ;  what  was  the 
amount  of  the  whole  ?  Ans.  456  dollars  25  cts. 

51.  A  lady  purchased  a  set  of  silver  weighing  51b.  6oz, 
5dwt.  at  1  dollar  50  cents  an  ounce;  what  was  the  cost  of 
the  whole  ?  Ans.  809  S7^  cts. 

52.  A  lady  intending  to  make  a  bed-quilt  containing  6 
square  yards,  desired  her  daughter  to  inform  her  how  much 
domestic,  o  quarters  of  a  yard  wide,  would  be  required  to 
line  the  same.     How  many  did  it  take?  Ans.  8yds, 

53.  A  pijte  will  drain  off  a  cistern  of  water  in  12  hours. 
iHow  many  pipes  of  the  same  size  wll  empty  it  in  30 
! minutes?  •  An^^  24  pipeb'. 
I  54.  A  gentleman  bought  a  bag  of  coffee  for  his  own  use, 
!  weighing  1271b.j  for  which  he  gave  15  dollars  25  cents. 

What  was  it  a  pound?  Am.  12  cts.  -f- 

55.  If  a  man  spend  4  dollars  62  J  cents  each  day,  how 
much  will  that  amount  to. in  a  year?       Ans.  1688  12^  cts. 

56.  I  lent  my  friend  350  dollars  for  five  months,  be  pro- 
mising to  do  me  the  same  favor,  but  when  requested,  he 
could  spare  only  125  dryllar.-.  How  long  ought  I  io  keep 
jit  to  balance  the  favor?  Ans.  14  monthi->. 

57.  If  a  person's  income  be  1000  dollars  a  year,  how 


DOUBLE  RULE  OF  THREE.  61 

much  can  lie   save  provided  he   spend  $1  50  cents  each 
day?  Ans.  452  dollars  50  cts. 

58.  If  the  third  of  six  he.  three,  what  may  one-fourth  of 
twenty  be?  As  2  :  5  :  :  3.         Ans.  7 J. 

59.  If  80  days  tuition  cost  3  dollars  50  cents,  how  much 
is  one  day  worth  at  that  rate  ?  Ans.  11  f  cts. 

60.  How  many  planks  6  inches  wide  and  12  leet  long 
will  it  require  to  lay  a  floor  that  is  18  feet  wide  and  24  feet 
long?  Ans.  72  planks. 

ol.  A  certain  boat  is  80  feet  long  and  18  feet  wide.  I 
demand  the  number  of  planks  re<:j[uired  to  floor  i  ,  18  feet 
long  and  1  foot  3  inches  wide  ?  Ans.  88  J.  -f- 

JVote.  The  diameter  of  a  circle  given  to  find  the  circum- 
ference. State,  if  7  give  22,  what  will  the  diameter  give  ? 
Or  the  circumference  given  to  find  the  diameter.  As  22  is 
to  7,  so  is  the  circumference. 

62.  K  a  wheel  be  20  feet  in  diameter,  what  is  its  circum- 
ference? 7:  20::  22.     (ijis.  62f. 

63.  If  a  wheel  be  60  feet  in  circumference,  what  is  its 
diameter  ?  22  :  60  :  :  7.     (Ans.  19.  + 


DOUBLE  RULE  OF  THREE. 

Double  Rule  of  Three  i8_that  in  which  five  terms  ai*e 
given  to  find  the  sixth  or  answer. 

HOLE. 

That  which  is  the  principal  cause  of  gain,  loss,  or  action, 
is  the  first  term.  Space  of  time  or  distance  of  place  the 
second.  The  gain,  loss,  or  the  action,  the  third.  Then 
place  the  other  two  terms  under  those  of  the  same  name. 
If  ihe  blank  fall  .under  the  third  term,  multiply  the  first  and 
second  terms  together  for  a  divisor;  the  other  thi^ee  for  a 
dividend.  But  if  the  blank  fall  under  the  first  or  second 
terms,  multiply  the  third  and  fourth  terms  together  for  a 
divisor;  the  other  three  for  a  dividend.  The  answer  will 
be  of  the  same  denomination  as  the  blank  term. 

J^ote.  If  the  blank  fall  under  the  third  term,  it  is  direct 
proportion,     If  under  the  fii-st  or  Eacoud,  inverse  proportion. 

6 


i 


ni     ■    ■  jiiii  ij      I    ^1     t^l      ■r  '        I     II  n«iiii     I  '■    ■.       .  —^M— i 

D(>LBLE   RULE   OF   THREE, 


MWiM'.irfn 


EXAMPLES. 

i      1.  If  6  men  iu  10  days  mow  60  acres  of  grass,  how  long! 
ijwill  it  take  5  meu  to  mow  80  acres? 

2.  If  7  men  am' reap  8-1  acree  of  whe^i  In  12  days,  bow 
many  men  c^n  reap  100  acre*  iu  6  days  ?  1 

men 


da.      A.  mtn.  da,      Ji. 

10  :  :  60  T  :  12  :  :  84 

80  5     100 

60                  10  12 


300  800  84     1200-    .. 

6      .  5  7 

;-'>j00)48|00  42|0)  840|0  (Am.  20  meu. 

84 


Ans.  16  daj-g. 


0 


3.  If  4  men  in  8  dayy  eat  5lb.  of  bread,  how  nmeh  will 
^12  men  ecit  in  20  days?  Ans.  37Mb. 

\     4.  Suppose  4  men  mow  48  acres  in  12  days,  how  many 
acres  can  8  men  mow  in  16  days?  Ans.  128a. 

!     5.  If  $100  gain  86  in  twelve  months,  what  will  ^400 
^gain  in  9  months?  Ans.  18  dollars. 

6.  If  .8  men  in  16  days  can  earn  96'  dollars,  how  much 
can"  12  men  earn  in  26  dayn  ?  Ans.  284  doilari^. 

7.  If  ten  men  in  18  days  can  earn  56  dollaxB,  how  many 
dollars  can  20  meu  earn  in  35  days? 

■     Ans.  $217  77ctti.  7m,  4- 

8   Suppose  8  men  can  make  i20  pair  of  shoes  in  30  days, 

how  many  can  12  men  make  in  90  daya  ?      Ans»  540  pair. 

9.  If  66  dollars  31.}  cents  be  the  wagen  of  20  men  for  5 
days,  what  will  46  meu  earn  in  32  days  ?      Ans,  $828  92ct6. 

10.  If  100  dollars  in  a  year  mrc  6  dollars  interest,  what 
will  335  dollars  give  in  3  years  ?       Ans.  60  dollars  30  cts. 

11.  "When  10  oxen  in  18  days  eat  2  acres  of  grass,  how 
many  acres  ^vill  serve  20  oxen  27  days?  Ans.  6  acres. 

12.  Sup|X!3e  the  wage??  of  6  person?,  for  21  weekM  be  288  , 
dollars,  what  must  14  persons  receive  for  46  weeks  ? 
I          /  Ans.  1472  dollars 

13.  If  STlb.  of  l^eef  be  suSicient  for  12  persons  4  days, 
how  many  pounds  will  suffice  38  men  16  days  ? 

hm  4681b.  lOfAT. 


— ^— ™^"'— — *— *— ^"^ '    .        ""■'*"  _i.   '     -.,^','T'-'J;3-l;^'■i" i 

I>OUBLi:    RULE    or    THREE.  (58 


14.  If  30  hoi*ses  in  4  days  eat  40  bushels  of  corn,  how 
many  bushels  will  suffice  100  horses  20  days  ? 

Ans.  666fbu. 

15.  If  the  carriage  of  9cwt,.  45  miles,  cost  54  dollars  54 
cents,  how  far  may  S6cwt.  be  carried  for  98  dollars  72  cts.  ? 

Ans.  20m.  2fur.  86p.  + 

16.  K  100  dollars  in  12  months  gain  6  dollars  interest, 
what  will  be  the  interest  of  400  dollars  for  14  months  ? 

Ans.  28  dollars. 

17.  If  100  dollars  in  12  months  gain  8  dollars  interest, 
what  sum  will  gain  50  dollars  in  24  months  ? 

Ans.  312  dollars  50  cts. 

18.  If  100  dollars  in  365  days  gain  6  dollars  interest, 
what  will  be  the  interest  of  1000  dollars  for  27  days? 

Ans.  4  dollars  44  cts.  nearly. 

19.  If  100  dollars  in  52  weeks  gain  10  dollars  interest, 
what  will  be  the  interest  of  75  dollars  for  7  weeks  ? 

Ans.  1  dollar  00 f  ct. 

20.  If  12  bushels  of  oats  be  sufficient  for  20  horses  22 
days,  how  many  biiBhels  will  serve  62  horses  86  days  ? 

Ans.  60bu.  3pe.  3qt.  Ipt.  4- 

21.  When  4  boys,  in  20  days,  collect  1500 'bushels  of 
apples,  how  many  days  will  it  require  25  persons  to  collect 
4000  bushels  ?    '      '      -  Ans.  8  days.  + 

22.  What  is  the  interest  of  568  dollars  for  4^  years,  at 
6  per  cent,  per  annum  ?  Ans.  152  dollars  01  ct. 

23.  What  will  be  the  interest  of  80  dollars  for  10  months 
at  10  per  cent.  ?  Ans.  6  doUara  66  f  cts. 

24.  If  100  dollars  in  12  months  gain  83  dollars  38^  cts., 
what  will  be  the  interest  of  64  dollars  for  8 J  months? 

Ans.  15  dollars  11  cts.  -f 

25.  If  100  dollars  in  one  year  gain  7  dollars  50  cents 
interest,  what  sum  will  gain  9  dollars  in  4  months  ? 

Ans.  360  dollare. 

26.  What  ifl  ihe  interest  of  19  (ioUars  for  5|  months  at 
6  per  cent.  ?  Ans.  49 1  cts.  -f 

27.  What  sum  at  6  per  cent,  will  produce  500  dollars 
interest  in  one  year?  Ans.  8333^  dollars. 

28.  A  gentleman  said  the  money  he  had  on  interest  at  6 
per  cent.,  produced  one  dollar  per  day.     What  sum  had  he] 
on  interest/  Ans.  6083 J  dollars. 

_^     29.  With  how  many  dollars  could  I  gain  6  dollars  in  one 


\U 


PRACTICE. 


year,  if  \vith  560  dollai's  I  gain  5G  dollars  in  one  year  and 


8  month t 


Ans.  100  dollars. 


30.  A  wall  wldch  is  to  be  built  to  the  height  of  40  feet 
has  been  raised  20  feet  in  10  days  by  16  men,  how  many 
men  muni  be  employed  to  finish  the  Tvork  in  5  days  ? 

Ana.  32  men. 


PRACTICE. 

Practice  is  a  phort  method  of  asceiiaining  the  value 
any  number  of  articles  at  any  given  price  per  article. 

TABLE  OF  ALIQUOT  PARTS. 


of 


cts. 

$ 

50  = 

■■  ^    ' 

25 

k 

20 

i. 

o 

12* 

i 

f*i 

10 

8^ 

1 

T2 

-  a^ 
o 

>— < 

6} 

tV 

n 

5. 

A 

4 

in 

*> 

1 

5U    J 

m. 

Cts. 

5  = 

■■  i  ] 

1       ^^ 

2 

1 

r  sfl 

1 

tV 

1  ^ 

2  or  56 

1  28 
16 
14 

8 
7 


CWL 

i 


■V 

I 


o 


CASE  I. 

u  *    < 

\     When  the  price  is  i,  I,  },  |,  or  f  of  a  cent  per  article, 
pound,  y^trd,  acre,  ])ushel,  &c. 

RULE. 

Divide  the  given  smn  or  fjuantity  by  the  aliquot  jjarts  of 
\  a  cent  for  the  answer  in  cents. 

EXAMPLES 

1.  Wlat  is  the  value  of  124  apples  at  ^  of  a  cent  each  ? 

2.  What  is  the  value  of  1260  peaches  at  ^  cent  each  ? 

i     1    124  *    J    1260 


Ans.     31  cents. 


Ans.     $6  30  cents. 


-^=^ 


r^ 


rRACTicii;. 


G5 


iJ..  What  is  the  value  of  192  plums,  at  |  of  a  cent  each  ? ! 

Ans.  S144cts.i 

4.  AVhat  in  the  value  of  24  quills,  at  J  of  a  ceut  each  ? 

Ans.  8  cents.  [ 

5.  \\Tiat  is  the  value  of  12  cherries,  ut  f  of  a  cent  ? 

Ans.  8  cents 

6.  How  much  will  29  come  to,  at  ^  of  a  cent  each  ? 

Ans.  7^  cents 

7.  How  much  will  11  come  to,  at  g  of  a  cent  each? 

Ans.  8^  cents 

8.  What  is  the  value  of  19,  at  J  cent  each  ?  I 

Ans.  9^  cents.  I 

9.  What  is  the  value  of  20,  at  2  mills  each? 

Ans.  4  cents. 

10.  What  is  the  value  of  40,  at  5  mills  each  ? 

Ans.  20  cents. 

11.  Wliat  is  the  value  of  30,  iit  I  mill  each  ?     Ans.  3  cts. 

CASE  2. 
Wlieu  the  giveli  price  is  cent8 : 

RULE. 

Divide  the  given  sum  by  the  aliquot  parts  of  a  dollar  for 
the  answer  in  dollars. 

EXAiMPLES. 

1.  What  is  the  value  of  3216,  at  6^  cents? 

2.  What  is  the  value  of  8620,  at  10  Cents? 


6^ 


I  0 


^^O 


216  (Ana.  $201. 


10 


32 


I 


8G20 


16 
16 


Ans.    $802 


3.  What  is  the  value  of  4260,  at  20  cte.  ?  Ana.  S52 

4.  8264,      20  1652 
6.                                   4264,       12  i  533 

6.  5876,      50  21*38 

7.  386,      25  96 

8.  18626,      55  10244 


cts.  m. 
00  0! 
80  0, 
00  0 
00  Oj 
50  0 
30  0, 


•m'         »ipa«fwa 


Ob 


PUACTIOE. 


9  What  ia  tHe  value  of  3542,  at  45  cts 

10.  1724,  37  J 

11.  31925,  80 

12.  3654,  18  J 
18.             13854,  56i 


$  cts.in 
?  Aub.  1593  90  0| 
646  50  Ol 
25540  00  0 
685  12  5 
7792  87  5 


CASE   o. 

When  the  gi>  ea  prici  ia  dollars  ftiid  «:cnf« : 

IIULE. 

,     Multiply  tlie  giveu  sum  by  the  dollars,  aud  take  parU  for 
Ithe  ocDts,  and  add  the  products  together  for  the  answer  in 

'  dollfirs. 


EXAMPLES. 


1.  What  IS  the  value  of  420  buBhcls  of  wheat,  at  1  dollaj- 
20  Wilis  per  biiyhel  ? 


20 


420 
1 

420' 
84 

504  dollars. 

$  CtS.  $       CtSM. 

2.  W^hat  is  the  value  of  2412,  at  2  06icts.  ?  Ans.  4974  75  0 

3.  1224,  3 12^  3825  00  0 
4. 
5. 
6. 
i . 
8.                       .    . 

CASE   4. 

When  the  gives  gum  consists  of  several  denominations, 
such  aa  yd.,  qr.,  na.,  &c. : 

RULE. 

Set  down  the  given  price  of  one  of  the  highest  denomina- 
tion, and  multiply  it  by  the  whole  of  the  highest  denomina- 


870, 

1181 

1033  12  5 

197, 

4  20 

827  40  0 

162, 

2  25 

364  50  0 

217, 

5S7a 

1166  37  5 

228, 

7  62^ 

9363  50  0 

PRACTICE.  G7 ' 

tion  given;  then  take  aliquot  parts  of  the  next  lowest  de 
nomination,  continually,  and  add  the  products  together  foi 
the  answer. 

EXAMPLES. 

1.   What  is  the  value  of  lOcwt.  2qr.  71b.  at  SIO  25  (xnU 
per  cwt.  ? 

$    cts. 
10   25 
10  cwt. 


qr. 

'J. 

i 

lb. 

"T 

t 

102    50 
5    12i^ 


64 

Ans.     S108    26^  cte.  -f 

2.  What  is  the  value  of  5cwt.  Iqr.  141b.,  at  2  dollars  50 
cents  per  cwt.  ?  Ans.  $13  43  f  cents. 

3.  What  is  the  value  of  7cwt.  oqr.  101b.,  at  4  dollars  15 
cents  per  cwt.  "^  Ans.  $32  86^  cents. 

4.  AVhat  is  the  value  of  780bu.  3pe.  2qt.,  at  J  dollar  17 
ctvs.  per  bushel  ?  Ans.  .$913  55  cents  + 

5.  What  is  the  value  of  129cwt.  Iqr.  101b.,  at  1  dollar 
5  cents  per  cwt.  ?  Ans.  $135  80  6m.  + 

6.  What  is  the  value  of  25cwt.  Iqr.  91b.,  at  1  dollar  75 
cents  per  cwt.  ?  Ans.  $44  32  cents,  -f 

7.  What  is  the  value  of  2qr.  141b.,  at  $27  10  cents  per 
c^^t.?  Ans.  $16  93 1  cents. 

8.  W^hat  is  the.  value  of  12cwt.  3qr.,  at  $40  20  cents  per 

^^^•''„,,  Ans.  $512  55  cents. 

.  9.  W  hat  in  the  value  of  19bu.  Ipe.  of  corn,  at  35  ct«.  per 

b"^h*5l  ?  ^  Ans.  0  dollars  73 f  cents. 

10.  What  is  the  value  of  810  oum^es  13dwt.  12ot.,  at 
12  J  cents  per  ounce  ?  Au^.  102  dollars  8^%ents 

11.  What  i.s  the  value  of  27jd3.  3qr.,  at  ^9  65  cents  per 
yai-d  ?  Ans.  207  dollars  78cts.  7m. 

12.  What  is  the  value  of  SGOyds.  Iq.,  at  84  cent*?  ppr 
y^'^^J  Ans.  722  dollars  61  cents. 

13.  What  IS  the  value  of  126yds.  2qr.  2ua.,  at  4  dollars 
75  cents  per  yard  ?  Ans.  601  dollars  46ct3.  8m.  + 

14.  What  is  the  value  of  17hhd.  15gal.  3qt.,  at  64  dol- 
lars 75  cenLs  per  hhd.  ?  An?,  1116  dollars  93cts.  7m. 


168         '  INTEEE8T. 

INTEREST. 

Interest  is  a  consideration  allowed  for  the  use  of  money, 
relative  to  which  are  4  particulars,  viz;  Principal,  Time, 
Rate  per  Cent,  and  Amount.  The  principal  is  the  money 
for  which  interest  is  to  be  received ;  the  rate  per  cent,  per 
annum  is  the  interest  of  100  dollars  for  one  year ;  the  time 
is  the  nuuaber  of  years  or  months,  &c.,  for  which  interest  is 
to  be  calculated;  the  amount  is  the  principal  and  interest 
added  together. 

CASE   1. 

To  find  the  int«3n3st  for  any  number  of  years,  or  years  and 
months. 

RULE. 

Multiply  the  principal,  consisting  of  dollars,  by  the  rate 
per  cent.,  and  that  product  hj  the  number  of  years ;  or  if 
there  be  months,  take  aliquot  parts  of  a  year,  cut  off  two 
figures  OR  the  right  of  the  product  for  cents  j  or  if  there  be 
cents  in  the  principal,  cut  off  one  figure  on  the  right  as  a 
remainder ;  one  more  for  mills ;  two  more  for  cents ;  those 
en  the  left  will  be  dollars. 

CAS£  2. 
To  find  the  interest  for  any  number  of  months. 

RULE. 

.  Find  the  interest  at  6  per  cent.,  by  multiplying  the  prin- 
cipal by  half  the  number  of  months ;  or  at  any  other  per 
cent.,  fiud  the  interest  at  6 ;  then  state,  if  6  give  that  inte- 
rest, what  will  the  per  cent,  you  wish  to  calculate  give,  and 
cut  off  figures  in  the  product  for  cents,  as  in  Case  Ist. 

CASE  8. 

To  find  the  interest  for  any  number  of  days. 

RULE. 

Multiply  the  principal  by  the  number  of  days  j  divide  the 
product  by  6,  the  quotient  will  be  the  interest  in  mills  at  6 
per  cent.  If  the  principal  consist  of  dollars  and  cents, 
destroy  2  figures  on  the  right  of  the  product ;  the  balance 


INTEREST. 


69 


nl 


will  be  ^tho  interest  as  before.  If  any  other  per  cent,  is  re- 
quired^ 'take  aliquot  parts  and  add  or  subtract^  according  a^ 
the  per  cent,  is  more  or  less  than  6. 

JVote.  Case  3d  is  estimating  360  days  in  a  year,  which 
will  make  the  interest  rather  large ;  it  may  be  more  accu- 
rately found  by  multiplying  the  principal  by  the  number  of  ^ 
days,  and  dividimr  the  'product  by  a  proper  divisor  in  the , 
following  tabie,  wnich  divisors  are  found  by  the  following 
stating : 

da, 
:  365 


per 

cent 

.      3          da. 

Thus:     4  :  100  :  :  365. 

Rate  per  cent.     Divisors 

4 

9125 

H 

8111 

1 

5 

7300 

!  » 

i).\ 

6636 

6 

6083 

6^ 

5615 

, 

0 

0000 

per  cent.     $ 
Again,  thus :  5  :  100 


Rate  per  cent. 
7 
7^ 

8 

8^ 
9 

9\ 
10 


Divisors. 
5214 
4866 
4562 
4294 
4055 
3842 
3650 


A  divisor  may  also  be  found  for  weeks  or  months,  by 
using  52  weeks  or  12  months  in  room  of  305  days. 

CASE  1.. 
EXAMPLES. 

1.  What  is  the  interest  of  $500  for  1  year,  at  6  per  cent. 
per  auniun  ? 

2.  What  is  the  interest  of  40  dollars  50  cents  for  one 
year  and  six  moiitlis,  at  six  per  cent,  per  annum? 


3 
500 
6 

Ans.  ^s'ojbOcts. 


moutlia. 
6 


3 

cts. 

40 

^0 

6 

243 

00 
1 

243 
121 

00 
50 

Ans.  33  64  cte.  5m. 


70  INTEREST. 


3.  What  is  the  intereat  of  400  dollare  for  ouo  year,  at  six 
perceut.  y  Ana.  24' dollars. 

4.  What  is  the  interest  of  600  dollars  for  one  year,  at  six 
per  cent,  per  annum  ?  Ans.  36  dollars. 

5.  What  is  the  interent  of  250  dollars  for  one  year,  at  five 
per  cent.  ?  Ans.  12  dollars  50  cents.  | 

6.  What  is  the  interest  of  61  dollars  for  one  year.,  at  six. 
per  cent.  ?  Ana.  8  dollars  6  cents. 

7.  What  13  the  interest  of  44  dollars  for  two  years,  at 
seven  per  cent,  per  annum  ?  Ans.  6  dollars  16  cts. 

8.  What  is  the  interest  of  90  dollars  for  thne  years,  ul 
five  per  cent.  ?  Ans.  13  dollars  50  cents. 

9.  What  is  the  interest  of  68  dollars  for  four  years,  at, 
four  per  cent.  ?  Ans.  10  dolhu-s  88  c^nts. 

10.  What  is  the  interest  of  1000  dollars  for  four  years,  at 
eight  per  cent.  ?  Ans.  320  dollars. 

11.  Wliat  is  the  interest  of  50  dollars  for  five  years,  at 
five  per  cent.  ?  Ans.  12  dollai's  50  cents. 

12.  What  is  the  interest  of  19  dollars  for  two  yeai*8,  at 
four  per  cent.  ?  Ans.  1  dollar  52  cent.^?. 

13.  What  will  he  the  interest  of  1772  dollai-s  for  two 
years,  at  six  per  cent.  ?  Ans.  212  dollars  64  cents. 

14.  How  much  interest  will  75  dollars  draw  in  five  years, 
at  4^  per  cent.  ?  Ans.  16  dollars  87  ^  ct-s. 

15.  What  is  the  interest  of  100  dollars  for  two. years  and 
six  months,  at  6  per  cent., per  annum?         Ans.  15  dollars. 

16.  What  will  be  the  interest  of  350  dollirs  fur  three 
years  and  four  months,  at  6  per  cent,  per  annum  l* 

Ans.  70  dollars. 

17.  What  will  be  the  interest  of  48  dollars  for  four  years 
and  one  month,  at  5  per  cent,  per  annum  ? 

Ans.  9  dollars  80  cents. 

18.  What  is  the  interest  of  64  dollai-s  for  one  yeai*  and 
seven  months,  at  7  per  cent,  pei*  annum  ? 

Ans.  7  dollars  9}  cents. 

19.  What  is  the  interest  of  14  dollars  for  four  years  and 
11  months,  at  7  per  cent.  ?  Ans.  4  dollars  Sl'i  cts. 

CASE  2. 
EXAMPLES. 

1.  What  is  the  interest  of  40  dollars  for  four  months,  at 
6  per  c^nt.  per  annum  ?  Ans.  80  cents. 


^Tl1 


INTEREST-  71 

2.  What,  is  the  iuterest  of  GO  dollars  for  6  months,  at  8 
j-K?!  cent,  per  aunum  ?  Ana.  2  dollars  40  cts. 


10  60 


o 


3 


80  cento.  0  :  8  :  :  180 

8 

6)1440 

e2  40 

3.  What  is  the  interest  of  18  dollare  hr  six  months,  at 
Isix  pjT  cent,  per  annum?  Ans.  SO  54  cents. 

4.  What  is  the  interest  of  50  dollars  for  eight  montha,  at 
,| seven  ptn-  cent,  per  annum?  Ans.  ^2  38f  cts. 

6.  What  is  the  interest  of  ^900  for  five  months,  at  five 
per  cent,  per  annum  ?  Ans.  18  dollars  75  cts. 

6.  What  is  the  interest  of  91  dollars  50  cents  for  four 
months,  at  4  per  cent. "/  Ans.  1  dollai*  22  cents. 

7.  W  hat  is  the  interest  of  80  dollars  for  five  mouths,  at 
seven  per  cent.  ?  Ans.  2  dolWs  06^  cents. 

»^ote.     When  the  amount  is  required,  add  the  interest  to 
the  principal. 

8.  What  is  the  amount  of  S62   50  c-ents  for  thirteen^ 
months,  at  6  per  cent,  per  annum  ?       Ans.  ^6Q  oGctg.  5m.  i 

9.  What  i*  tlie  interest  of  tlir  for  fourteen  months,  at  sixi 
per  cent.  ?  Ans.  5  dollars  25  ccnte.; 

10.  What  is  the  intcrefct  of  S5  60  cents  for  5^  mouths,- 
at  six  per  cent,  'r  Ans.  15  cents,  -f- 

A\)le.     in  this  case,  after  finding  the  iuterest  at  six  per 
I  cent.,  if  any  other  r.at^  per  cent,  be  required,  take  aliquot' 
parts  and  add  cir  subtract,  ac<v)rdif»g  as  the  rate  per  cent,  is! 

more  or  lers  than  six.  -.  i 

I 

11.  What  is  iheintorept  of  80  dollars  fnr  eight  moutBaJ 
I  fit  five  p:i-  c€ij'.  " 


72 


INTEREST. 


12.  What  is  the  iutorest  of  00  dollars  for  four  mouths,  at 
eight  per  eont.  ? 


6  ptJF. 

5  por. 
1 


80 
4 

320  int.  at  6  per  ot. 
53^ 


60 
o 


^        3 


1  20  int.  at  6  per  ct 
40 

$1  60  cents. 


Ans.  $2  66f 


13.  Wliut  in  tlie   iutercBt  of  120  dollars  60"  cents  for 
fifteen  months,  at  6  pt-r  cent.  ?         Ans.  9  dollars  4ctH.  5m. 

14.  What  is  the  interest  of  5420  dollars  for  17  montlis, 
at  4  per  cent,  per  annum  ?  Ans.  307  dollars  13  J  cts. 

.  15.  What  is  the  interest  of  7200  dollars  for  14  months, 
at  G  per  cvjit.  per  anniun  ?  Ans.  504  dollars. 

16.  Yvliat  is  the  interest  of  8050  dollars  SDj  cents  for 
47  months,  at  6  per  cent.^  per  annum  ?  ' 

Ans.  1891  dollars  95cts.  5m. ! 

17.  What  is  tlic  interest  of  948  dollars  62^  cents  for' 
eight  months,  at  8  per  cent,  per  annum  ? 

Ans.  50  dollars  59  cents.  4-  , 

18.  What  is  the  interest  of  36  dollars  for  one  month,  at, 
8  per  cent,  j^er  ami  urn  ?  *  Ans.  24  cents, 

j      ]9.  What  is  the  interest  of  1000  dollars  for  40  months,' 
■  at  0  per  cent,  per  annum  ?  Ans.  200  dollars. ! 

!      20.  What  is  the  interest  of  328  dollars  for  12  months,  at  i 
6  p.r  cent.  ?  Ans.  19  dollars  68  cents* 

i  "  1 

!      When  there  is  a  fraction  in  tlie  rate  per  cent.,  un  5i,  6^, 
I  or  6 1,  multiply  and  add  i  or  A,  (tui  the  case  may  be,)  of  the 
I  pnncipal  to  the  product,  and  proceed  as  before. 
i 

i     21.  What  will  be  the  interest  of  540  dollars  for  24 
months,  at  5  per  cent,  per  alinum  ?  Ans.  54  dollars. 

22.  What  would  be  the  interest  of  482  dollars  for  84 
mouths,  at  6  dollars  per  c«nt.  per  annum  ? 

Ans.  202  ddln-?^  44  cts. 


aam 


SS=B 


INTEREST.  '  78 

2S.  "What  is  the  interest  of  325  dollars  for  60  months,  at 
4  per  cent,  per  annum  ?  Ans.  $54  16  cents  6in. 

24.  What  is  the  interest  of  840  dollars  for  63  months,  at 
4  per  cent,  per  annum  ?  Ans.  $176  40  cents. 

25.  What  is  the  interest  of  840  dollars  for  64  months,  at 
7  per  cent,  per  annum  ?  Ans.  $313  60  cents. 

26.  What  is  the  interest  of  560  dollars  for  4  months,  at 
six  per  cent,  per  annum?  Ans.  $11  20  cents. 

27.  What  is  the  interest  and  amount  of  100  dollars  for 
ten  months,  at  10  per  cent,  per  annum  ? 

Answer  i      ^^  ^^^  ^^'^'^- 
\  $108  33^  amount. 

28.  What  is  the  amount  of  76  dollai-s  25  cents  for  25 
months,  at  6  per  cent,  per  annum  ?     Ans.  $85  78cts.  Im.  + 


CASE  3. 

JVote.  Multiply  any  principal  hj  the  rate  per  (;ent.,  and 
that  product  by  the  nuniber  of  day  3  it  haa  been  or  interest, 
and  divide  the  last  product  by  366.  The  quotient  will  bo 
the  interest. 

EXAMPLES. 

1.  What  is  the  interest  of  1000  dollars  for  five  days,  at  6 
per  cent,  per  annum ?  Ans.  83  certs  3m.  + 

2.  What  is  the  interest  of  500  dollars  for  60  days,  at  8 
per  cent,  per  annum  ?  Ans.  $6  66cts.  6m.  + 


1000  500 

5  60 


6)5^0  6)30000 

8313^  2  Tr5"000 

I  10665 

6|66|6f 

3.  What  is  the  interest  of  400  dollars  for  40  days,  at  6 
per  cent,  per  annum?  Ans,  $2  66c^.  6m.  -|- 


'i  INTEREST. 

4.  Wh'di  is  the  interest  of  900  dollars  for  fourteen  dajs, 
Ut  6  per  cent.  '•  Ans.  $2  10  ceiilvS. 

I     5.  What  is  the  interest  of  1000  dollars  for  4  days,  at  61 
I  per  cent.  ?  Ans.  66f  cents,  j 

6.  What  is  the  interest  of  500  dollara  for  one  dav,  at  6 
pcT  cent.  ?  Ans.  8  cents  ';}m.  4- 

7.  What  in  the  interest  of  16  dollars  33J  cente  for  24 
dsys,  at  6  per  cent.  ?  Ans.  6  cents  5ra.  -\- 

8.  What  is  the  inteiHist  of  C4  dollars  64  cents  for  IS  days 
^ai  6  per  cent,  per  annum  ?  Ans.  19  cents  Sm.  \ 

9.  What  is  the  interest  of  45  dollars  for  22  days,  at  5i 
jp^T  cent,  per  annum?  Ans.  15  cents. -f 

10..  AVhat  is  the  interest  of  90  dollars  for  51  days,  at  8 
{A^r  cent,  per  annum  ?  Ans.  1  dollar  2  cents. 

JVoie.  AVhen  Uio  time  is  years,  months,  and  days,  pro- 
ofed witli  the  years  and  months  as  in  Case  Int,  and  for  the 
tUya  take  niiquot  parts  of  30. 

11.  What  is  the  interest  of  50  dollars  for  1  year,  2  months, 
and  5  days,  at  G  per  cent,  per  annum  ?         Ans.  $3  54  cents. 

12.  What  is  the  interest  of  100  dollars  for  one  year,  7 
months,  and  11  days,  at  6  per  cent.  ?      Ans.  $9  68  cents.  + 

13.  What  is  the  interest  of  21  dollars  for  4  years,  4 
mt-nths,  and  4  days,  at  5  per  cent. '/       Ans.  $4  56  cents.  + 

14.  What  is  the  interest  of  5  dollars  for  10  years,  3 
months,  and  19  days,  at  6  per  cent.  ?     Ans.  ^3  09  cents.  + 

15.  What  is  the  intei'eet  of  5  dollars  87^  cent*  for  9 
monthp,  and  24  days,  at  6  prr  cent,  per  annum? 

Ans.  28  rentf-i  7)ri.  f 

OASJE  4. 

The  amount,  time  and  rate  per  cent,  given  to  find  the 
principal. 

Find  the  amount  of  100  dollai-s  at  the  rate  ix>r  cent,  and 
time  given,  y,'hich  amount  is  the  first  term ;  the  gi^cn  sum 
.  the  2d ;  100  dollars  the  3d ;  proceed  by  the  Rule  of  Three ; 
■  the  quotient  will  be  the  principal  required.  j 


INTEREST.  75 


EXAMPLES. 

1.  What  principal  at  interest  for  8  years,  at  5  per  cent., 
will  amount  to  840  dollars  ? 

$  140  :  S40  :  :  100 

100  100 


Tv 


500  84 

8 


14fO)8400IO(AaF.  $600. 


00 

Intx^rost.     40100 
100 

Amount.    140 

2.  "What  principal  at  interest  for  5  years,  at  0  per  rent, 
per  iinuuni,  will  amount  to  650  dollars  ?  Ans.  $500. 

3.  What  principal  at  interest  for  5  years,  at  6  per  cent, 
per  annum,  will  amount  to  2470  dollars  ?  Ans.  $1900. 

CA8E  5. 

To  find  the  rate  per  cent,  when  the  amount,  time  nnd 
principal  arc  given. 

RULK. 

Subtract  the  principal  from  the  amount;  then  state  if  the 
principal  give  the  inlerest  or  remainder,  what  will  100  dol- 
lars give.  Divide  the  answer  by  the  number  of  years ;  the 
quotient  will  be  the  rate  per  rent. 

1.  At  what  rate  per  cent,  per  annum  will  $500  amount 
t<i  8^50  in  five  years  ? 


Aiuuuot.    650 
Principal.  500 

V                      v                       9 

500     :     100    •    •    150 
150 

150  intorejit 

5000 
100 

5010)150100 
Years.  5)30 

Ans.  0  per  cent. 

J 


20|00  .  210)1210 

Ans.  6  years. 

2.  In  what  time  will  COO  dollars  amount  to  798,  at  6  per 
cent,  per  annum?  Ans.  5 J  years. 

3.  Suppose  1000  dollai's,  at  4^  per  cent,  per  annum, 
amount  to  1281  dollars  25  cts.,  liow  long  was  it  at  interest? 

Ans.  6  years  3  months. 

PROMISCUOUS   EXAMPLES, 

1.  What  is  the  interest  of  500  dollars  for  one  year  and 
2  months,  at  6  per  cent.  ?  Ans.  35  dollars. 

2.  What  is  the  interei^t  of  450  dollars  for  2  years  and  6 
months,  at  5  per  cent.,  per  annum  ?     Ans.  50  dollars  25  cts. 

3.  What  is  the  inter 3st  of  65  dollars  87 J  cents  for  9 
months,  at  6  per  cent.  ?  Ans.  2  dollars  06^  cts. 

4.  What  m  the  interest  of  800  dollars  for  Ibur  years,  5- 
months  and  19  days,  at  G  per  cent,  per  annum  ? 

Ans.  214  dollai-s  53cts.  3m.  + 

5.  AVI.  at  is  the  interef  t  of  18  dollars  75  cts.  for  1  year,  2 
months  aid  7  days,  at  6  per  cent,  per  annum? 

Ans.  1  dollar  33^  cents. 


70  INTEREST.  i 

2.  At  what  rate  per  cent,  will   600  dollars  amount  to 
3744  in  bur  years  ?  Ans.  6  per  cent. 

4.  If  S84  dollars,  a<   intere;3t  2  years  aijd  6  months,  | 
amount    o  $927  82^  c  s.,  what  was  the  nite  per  cent,  per 
jinnum?  Ans.  4^  per  cent, 

CASE  G. 

To  find  the  time  when  the  principal j  amount,  and  rate  per' 
cent,  are  given. 

RULE. 

Divi'^^  the  whole  interest  by  the  interest  of  the  principal, 
for  one  year.     The  quotient  will  be  tho  time  required. 

1.  In  what  time  will  400  dollars  amount  to  520  dollars, 
at  5  per  cent,  per  anuun/  ? 

409  520 

5  400 


AND   BROKERAGE. 


r-^    I 


C.  What  is  tliG  interest  of  90  dollars  for  8  month?,  at  9 
per  cent.  ?  Ans.  5  dollars  40  cts. 

7.  What  is  the  interest  of  6  dollars  for  G  days,  at  6  per 
cent.  ?  An 8.  6  mills. 

8.  V/hat  is  the  amount  of  1000  dollars  25  cts.  f  )r  4  years, 
\  months,  and  5  days,  at  7^  per  cent,  per  annum? 

Ans.  1326  dollars  37  cts.  3m.  + 

0.  In  what  time  will  1000  dollars  amount  to  1500  dollars, 

at  8  per  cent,  per  annum  ?  Ans.  6  years  3  months. 

10.  What  is  the  interest  of  25  cts.  for  25  years,  at  6  per 
cent,  per  annum  ?  Ans.  37  J  cts. 

11.  What  is  the  interest  of  87  J  cents  for  1  year  and  6 
months,  at  6  per  cent,  per  annum  ?  Ans.  7  cts.  8m.  -f- 

12.  At  wliat  rate  per  cent,  per  annum' will  1200  dollars 
amount  to  1800  dollars  in  5  3'ears  ?  Ans.  10  per  ct. 


INSURANCE,  COMMISSION,  AND  BRO- 
KERAGE.- 

Brokerage  is  an  allowance  to  insure  factors  and  brokers 
at  a  stipulated  rate  per  cent.,  agreed  on  by  the  parties  con- 
cerned. 

RULE- 

INIultiply  the  sum  by  the  rate  per  cent.  If  the  rate  be 
less  than  one  per  cent.,  take  aliquot  parts. 

EXAMPLES. 

1.  What  is  the  commission  on  500  dollars,  at  5  per 
cent.  ?  • 

2.  What  is  the  commission  on  400  dollars,  at  f  dollars 
per  cent.  ? 

$  s 


500 

5 

Ans.  $257)0 


k 


400 


200 
100 


Ans.  83  00 


]  7S  DISCOUNT. 

8.  What  is  the  ineurance  of  GO  doUai-s,  at  3  per  cent. '/ 

An£.  1  dollar  SO  cents. 

4.  What  is  the  commiseiuil  on  1351  dollars  50  cents,  at 
5  J  per  e«nt.  ?  Aus.  74  dollars  33  cents. -f 

5.  The  gales  of  certain  g<X)d3  amount  to  1080  dollars, 
what  smn  is  to  be  received  for  them,  allowing  2|  per  cent, 
for  commission?  An.s.  1633  dollars  80  cents. 

6.  What  is  the  commiseioii  on  3450  doilai*8,  at  4  J  per 
cent.  ?  Ans.  155  dollars  25  cents. 

7.  When  a  broker  sells  good.«  to  the  ainoimt  of  984  dol- 
lars 50  cents,  what. is  his  commigsion,  at  1}  per  cent.  ? 

Ans.  12  dollars  30  cents  Cm.  -}- 

8.  What  is  the  insurance  of  1250  doilars.  at  7i  per  cent.  ? 

Ans.  03  (lollai's  75  cents. 
0.  If  a  broker  buys  goods  for  me,  .nmoimting  to  1650 1 
■  dolhu-B  75  QQnUi,  what  sum  must  I  ])ay  hiin,  allowing  1^ 
per  cent.  ?  AuB.  24  dollars  76  ccnl^  lm.--[- 

10.  What  if:  the  commission  on  a  pnlc  of  goods,  amount-; 
ing  to  1184  dollars,  at  5  per  cent.  ?     Ans.  59  dollars  20  cts. 

11.  What  is  the  commission  on  a  sale  of  goods,  amount- 
J i«g  to  4820  doUars,  at -4*  per  cant,? 

Ans.  21C  dollars  90  cents. 


DISCOUNT. 

Discount  is  an  allowance?  made  for  the  payment  of  a  sum 
of  money  before  it  becomes  due,  and  is  the  difference  be- 
tween that  sum  due  sometime  hence  aiid  its  prt^scnt  worth. 

RULE. 

Find  the  interest  Qjf  100  dollars  at  the  per  cent,  and  tii*e 
given ;  to  this  interest  add  100  dollara,  which  amount  is  the 
first  term  ;  the  given  sum  the  second  j  100  dollars  the  third. 
Proceeil  by  the  Kule  of  Three.  The  answer  will  be  the 
present  worth.  Subtract  the  answer  from  tlie  given  sum, 
and  the  remainder  will  be  the  discount. 

EX^iMPLES. 

1.  What  is  the  discount  of  500  dollars  for  4  ye^rs,  dis- 
count at  5  por  cent,  per  annum  ? 


MUK-^.^*  ■3»^^|l^klSa^a<MlMW!Wt3MMnM<M«»»CI<IBB«a».'*t^S^ 


DISCOUNT. 

$ 

100 
5 

500 
4 

20100 
100 

120  :  500  :  :  100 
100 


1210)500010 

prcbciit  worth.     41 G  66| 

S  cts. 
500  00 
416  (>G^ 


\  Discount.     S83  33^1 


2.  Wiiat  is  the  present  worth  of  GOO  dollars,  due  m  2 
3'curs,  diacouut  at  6  per  cent,  per  annum? 

Ans.  $535  7 lets.  4m.  -|- 

3.  What  is  tiie  discount  of  590  dollars  for  2  years,  dis- 
count at  6  per  cent,  per  annum  ?  Ans.  $63  21  ^  ct>i. 

4.  "SVhat  is  the  present  worth  of  480  dollars,  due  in  4 
years,  at  4  per  cent,  discount?       Ans.  413  dollars  79icts.  + 

5.  "What  is  the  discount  of  645  dollars  for  9  months,  at 
6  per  cent,  per  annum  ?  Ans.  $27  77ct6.  6m. 

6.  What  is  the  present  worth  of  580  dolhirs,  due  in  8 
moaths,  discount  at  6  per  cent,  per  ;innum? 

Ans.  557  69  cents.  + 

7.  What  is  the  present  vrorth  of  775  dollars  50.  cents, 
due  in  4  years,  at  5  per  cent,  per  annum  ? 

Ans.  $640  25  cents. 

8.  TJouglit  goods  amounting  tu  iilT)  dollars  75  cent,-^,  at  6 
months'  credit,  how  nuich  ready  money  nmst  be  paid  if  a 
discount  of  4^  per  cent,  be  allowed?  Ans.  $602  20  cts. 

9.  Bought  goods  amounting  to  000  dollarp,  ao  4  years' 
credit,  how  much  ready  money  mw.i  be  jjaid  if  a  discount 

lof  6  per  cent,  be  allowed?  Ans.  $725  80 i  cent6. 


8*0  TARE   AND    TRET. 

]  0.  What  is  the  discount  of  00  dollar*  for  1  year  and  ^6  \ 
months,  at  6  per  cent,  per  annum?  Ans.  $7  43 J  ccntp. 

■  n.  What  is  the  discount  of  205  dollars,  duc^in  15 
months,  at  7  per  cent,  per  annum?       Ans.  $,16  49^  cts.  + 

12.  A.  owes  B.  100  dollars,  due  in  one  year,  but  B. 
agrees  to  allow  A.  a  discount  of  25  per  cent,  per  annum  for 
presen<}  payment.     What  sum  will  discharge  the  debt  ? 

Ans.  80  dollars. 

13.  What  is  the  discount  of  100  dollai-s,  due  in  12 
months,  at  25  per  cent,  per  annum?  Ans.  20  dollars. 

JYoie.  When  discount  is  made  without  regard  to  time,  it 
is  found  precisely  like  the  interest  for  one  year. 

14.  What  is  the  discount  of  800  dollars,  at  6  per  cent.  ? 

15.  What  is  the  discount  of  99  dollars,  at  5  per  cent.  ? 

*$  V 

800  99 

6  5 


Ans.  $48  00  discount.  Ans.  U  95 

16.  What  is  the  discount  of  476  dollars,  at  8  per  cent.  ? 

Ans.  14  dollars  28  cents. 


TARE   AND   TRET. 

Tare  and  Tret  are  certain  allowances  made  by  merchants 
in  selling  their  goods  by  weight.  Tare  is  an  allowance 
made  for  the  weight  of  the  barrel,  box,  &c.,  that  contains 
the  commodity  bought.  Tret  is  an  allowance  of  4  lb.  in 
every  104  lb.  for  waste,  dust,  &c.  Gross  weight  is  the 
goods,  together  with  the  barrel,  box,  or  whatever  contains 
them.  When  the  tare  is  deducted  from  the  gross,  what  re- 
mains is  called  suttle.  Neat  weight  is  the  weight  of  articles 
after  all  allowances  are  deducted. 

RULE. 

ist.  Subtract  the  whole  tare  from  the  whole  gross ;  the 
remainder  will  be  neat.  -2nd.  When  the  tai*e  is  so  much 
per  barrel,  box,  &c.,  multiply  the  tare  per  barrel,  box,  &c., 


TARE    AND    TRET. 


81 


by  tlic  minibGr  of  barrels,  boxes,  &c.     The  product  will  be 

the  whole  tare.     Subtract  the  whole  tare  from  the  whole 

'grop?^,  and  the  remainder  will  be  neat.     3d.  When  (he  tare 

is  so  iiiiich  per  cwt.,  run  aliquot  part,  or  parts  of  a  cwt., 

through  the  whole  gross.     Subtract  the  quotient  tlicrefrom, 

and  the  remainder  will  be  neat.     4th.  Wheii  tret  is  allowed 

with  tare,  subtract  the  tare  from  the  gross,  as  before.     The 

SI  remainder  will  be  suttlc...  Divide  the  suttle  by  26.     The 

mjuotient  will  be  tret.    Subtract  tlie  tret  from  the  suttle,  and 

!  the  remainder  will  be  neat. 


EXAMPLES. 

1.  What  is  the  neat  weight  of  a  hogshead  of  toba<;co, 
weighing  2cwt.  3qr.  251b.  gross,  tare  in  all  Icwt.  2qr. 
121b.  ? 

*  cwt.  qr.   lb. 

2     3     25  gross. 
1     2     12  tare. 


Ans.     1     1     13  neat. 

2.  What  is  the  neat  weight  of  a  hogshead^  of  tobapco, 
weio-hintr  5cwt.  2qr.  151b.  gross,  when  the  tare  is  3qr.  71b.? 

°      ^  ^  Ans.  4cw^t.  8qr.  81b. 

3.  What  is  the  neat  weight  of  369cwt.  2qrs.  211b.  gross, 
tare  in  the  whole  lOcwt.  Iqr.  121b.  ? 

Ans.  359cwt.  Iqr.  91b.  | 

4.  What  is  the  neat  weight  of  0  hogsheads  of  sugar,, 
each  weighing  4cwt.  Iqr.  41b.  gross,  tare  in  the  whole 
IScwt.  3qr.  191b.  ?  ! 

civt.  qr.    lb. 

4      14 

6 


25      2    24  whole  gross  weight. 
13      3    19  whole  tare 


11      3      5  neat 

5.  How  much  is  the  noa't  weight  of  7  casks  of  indigo, 
each  weighing  ocwt.  2qr.  121b.  gro.ss,  tr.re  251b.  per  cask  ? 


TARE   AND   TKET. 


ciot.  qr.  Ih.  cwt.  qr.  Ih. 

3     2    12  0     0    25 

7  7 


•  25     1      0  gross.  12      7  tare  in  all. 

12      7 


Ans.  23     2    21  neat. 

6.  What  is  the  neat  weight  of  G  casks  of  raisins,  each 
weighing  3cwt.  2qr.  101b.  gross,  tare  201b.  per  cask  ? 

Ans.  20cwf.  Iqr.  241b. 

7.  What  is  the  neat  -weight  of  35  keg«  of  figs,  gross 
weight  37cwt.  Iqr.  20ib.,  tare  per  cwt.  141b.  'I 

cwt.  qr.   lb 


lb. 
14 


^ 


37     1     20 

4     2     20  quotient. 


Ans.  32     a     00  neat 

8.  What  is  the  neat  weight  of  6  hogsheads  of  sugar,  each  ij 
weighing  7ewt.  3qr.  141b.  gi'oss,  tare  201b.  per  cwt.  ? 

Ans.  oScwt.  3qr.  71b. 

9.  What  is  the  neat  weight  and  value  of  12  bags  of  coifee, 
each  2cwt.  Iqr.  lOlbs.  gross,  tare  181b.  per  cwt.,  ti'et  41b. 
per  1041b.,  at  19  dollars  60  cents  per  cwt.  ? 


.  (  22cwt.  2qr.  181b.  neat. 

^^^^^^•444  dollars  15 


I  444  dollars  1 5  cts.  value. 

10.  What  is  the  cost  of  24  casks  of  prunes,  each  cask 
weighing  Icwt.  Iqr., 231b..  gross,  tare  181b.  per  cask,  at  5 
dollars  17 f  cents  per  cwt.  ?  Ans.  $100  79cts.  4m. 

11.  Wliat  is  the  neat  weight  of  5  hogsheads  of  sugar, 
eaeh  lOcwt.  Iqr.  201b.  gross,  tare  3qr.  251b.  per  hogshead, 
tret  41b.  per  1041b.? 

civt.  qr.  lb.  cwL  qr.  lb. 

10    1    20  0    3    25 

*      5  5 


52    0    16  gTose.  4    D    13  bre. 

'4    3    13  tare. 


Divide  by  26)47    1      3  sutflo. 

13       7  tret  quotient. 

An;^.  45    1    24  neat. 


EQUATION. 


83 


To  find  the  neat  weight  of  Pork,  CBtahlished  hv  custom, 
when  the  gross  is  given. 

RULE. 

Place  each  hundred  separately.  Then  subtract  i  or  25 
from  the  firat  hundred :  ^  or  12^  from  the  second  hundred. 
The  remainders  will  be  neat.  All  over  the  second  hundred 
is  neat.  Add  the  remaindei-s  and  all  over  the  second  hun- 
dred together  for  the  neat. 

Note.  \  must  be  taken  from  any  number  oi  pounds  L'ross, 
under  100  including:  —  ^  from  all  over  lOa  pounds^  and 
under  200  including. 

EXAMPLES. 

1.  What  is  the  neat  of  a  hog  weighing  184  pounds  gross  ? 

2.  What  is  the  neat  of  a  hog  weighing  212  pounds  gross  ? 


25 


\ 


100  12.^ 
25 


i 


84    25 
10* 


\ 


100  12* 
25 


I 


100  12 
12  J 


7d 
73 1 


73J 


75 

87* 
12 


87J 


Ans.  148^  Neat. 

Ans.  174»}  Neat. 

3.  What  is  the  neat  of  a  hog  weighing  305  pounds  gross  ? 

Ans.  267  *lb.  neat. 

4.  What  is  the  neat  of  3  hogs  weighing  gross  as  follows, 
Az. :  no.  1,  191  lb. ;  no.  2,  76  lb. ;  no.  3,  201  lb.  ? 

Ans.  375  i  lb.  neat. 

5.  What  is  the  neat  of  2  hogs  weighing  gross  as  follows, 
•iz.  :  no.  1,  219  lb. ;  no.  2,  1 13  lb. :'      Ans.  268  lbs.  neat. 


EQUATION. 

EquatJuii  hi  used  to  find  fhe  menu  time  of  aeverol  pay- 
jments  du.-i  at  dilL'reiit  times. 

RULE. 

Multiply  each  payment  by  its  time.  •  Add  up  the  several  i 
products,  and  divide  the  sum  by  the  whole  debt. 


[j  proc 


84  EQUATION. 

EXAMPLES. 

1.  A.  owes  B.  (^0  dollaifj,  of  which  40  dolhirg  is  to  l)e; 
paid  at  0  montlis,  aud  20  dollars  at  3  months,  hut  thoy  agree 
that  the  whole  shall  be  paid  at  one  tiuic.  When  must  it 
bo  pa\fi? 

S 

40x0=240 
20x3=  60 

6|0)30|0 

Aus.  5  mouths. 

2.  C.  owes  P.  nSO  dollar.s,  of  which  100  dollars  i.s  (u  bo 
paid  at  G  months,  120  dollar.s  at  7  months,  and  1(30  dollar.^ 
at  10  month?,  Init,  they  agree  that  the  whole  shall  he  paid 
at  one  time.     When  must  it  be  paid  ?     Aus.  8  months. 

3.  A  merchant  has  owing  to  him  300  dollai*s,  to  be  paid 
as  follows,  viz.  :  100  dollars  at  2  months  ;  100  dollars  at  4 
months;  100  dollars  at  G  months;  but  they  agrca  that  the 
whole  shall  be  paid  at  one  time.     When  must  it  bo  paid-? 

Ans.  4  months. 

4.  A  merchant  had  pm-eliased  goods  to  the  amount  of 
2000  dollars,  of  wliich  sum  400  dollars  are  to  be  paid  at 
prcKint,  SOO  dollar.^  at  G  mwuth?-,  aud  the  rest  at  1)  mOMthi; 
but  it  is  agreed  (<>  iJiake  t»nc  pa}  m.  lit  of  the  whole.  Whvn 
must  it  bo  paid?  Ans.  G  months. 

o,  A.  owes  J.  o(M)  doliar.s  whi(  h  will  be  duo  f<'ur  months 
hence.  It  is  agreed  that  100  dollars  hhall  be  p:iid  now,  aud 
that  the  rest- remain  unpaid  a  longer  time  than  four  months. 
When  must  it  bo  paid  ?  Ans.  6  months. 

G.   A.  owes  B.  100  dollnrs,  of  which  75  dollars  is  to  be 
paid  at  4  months,  and  25  (hdlars  at  2  months;  but  th^y 
aLOto  that,  the  whole  shall  b<'  jKud  at  one  time.       Whoni 
m\u'-t  it  he  paid  ?  An.-^..  3  A  montili^ 

7.  C.  is  indebted  to  a  merchant  to  the  amount  of  2500! 
dollars,  of  which  1000  dollars  is  payable  at  the  end  of  4^ 
months,  800  dollars  in  8  months,  and  700  dollar.-  in  12 
»tionths;  when  ofiglit  payment  to  be  made  if  all  are  paid 
i"!tnrrcriici-y  An'?.  7^  months. -f 


BARTER. 


BARTER. 


Wi 


Barter  is  the  exchanging  of  one  commodity  for  another, 
according  to  a  certain  price  or  value  agreed  on  by  the  parties 
concerned.  Questions  in  Barter  may  be  solved  by  the  Rule 
of  Three. 

When  any  articles,  at  a  given  price  per  article,  are  to  be 
bartered  for  any  other  articles,  at  a  given  price  per  article. 

RULE. 

Find  the  value  of  the  articles  whose  quantity  is  given. 
Then  find  how  many  of  the  other  articles  may  be  bought 
with  that  money. 

EXAMPLES. 

1.  A.  has  400  yards  of  cloth,  at  20  cents  per  yard,  for 
which  B.  is  to  give  him  books,  at  50  cents  each.  How 
many  books  must  A.  receive  ? 

2.  C  has  100  bushels  of  wheat,  at  75  cents  per  bushel, 
for  which  D.  is  to  give  him  rye,  at  37^  cents  per  bushel. 
How  many  bushels  of  rye  ought  C.  to  receive? 

cts.     cfs.         yd.  cts.      cts.  hu. 

50  :  2t  :  :  400  37J  :  75  :  :  100 

400  2  2 

5|0)800IO  75       150 

100 

Ans.  160  books.  


75)15000(Ans.  200  bu. 
150 

00 

8.  M.  has  500  barrels  of  flour,  at  6  dollars  per  barrel,  for 
which  II.  is  to  give  him  salt,  at  1  dollar  25  cents  per  bushel. 
How  many  bushels  of  salt  ought  M.  to  receive '/ 

Ans.  :'  100  l)u. 

4.  A.  has  20  pounds  of  sugar,  at  12  J  cents  per  pound,  for 
which  J.  is  to  give  him  fowls,  at  10  cents  a  piec( .  How 
many  fowls  ought  A.  to  receive  ?  An.s.  25  fowls. 


liARTEIl. 


5.  How  many  Imshulb  uf  rycj  at  40  cents  per  bushel,  lU'e 
iL^oiial  to  00  busi;  I.s  of  wtoat^at  i:0  .cents  per  biislicl? 

Ads.  112  .Iba. 

iy.  0.  hab  ICO  yards  of  ;5tati.  at  14  cents  per  ^-ayd,.  f'r 
which' N.  agrees  to  give  him  oats,  at  220  cent.s  per  Ini^h!  I. 
How  many  bushels  of  oats  ought  Q-.'to'  receive? 

Aili.  .liliDU. 

7.  P.  sold  108  yards  of  calico,  at  10  cents  per  yattl,  for 
Tvhieh  E.  gave  him  6  dollars  in  money,  and  the  rost^in  iiax- 
seed,  at  8  cents  per  bushel.  Kow  many  bushels  of  ihixseed 
did  P.  receive  ?  .    .  Au.s.  GObu. 

8.  How  many  pounds  of  tea,  at  80  cents  per  pound,  must 
be  given  in  barter  for  25  poiinds'of.  coffee, 'at  22  J' cents  per 
pound?  "    ^■'■•"     '■'■  ^" ''.''AnsrlSf  pounds. 

0.  A  merchant  has  1000  yards  of  cauvciss,^fit  20  cents  j)er 
yard,  which  he  is  to  barter  for  vsergc,  at  22 Jt  cents  per  yard. 
How  manv  vanls  of  serge  should  lie  receive? 

Ans.  88 8||  yards. 

10.  A.  LVdo  fjugar  at  12^  cents  per  pound,  for  a  quantity 
of  which  C.  is  to  give  him  450  pounds  of  tea,  at  1  dollar 
per  pbund.     How  much  sugar  must  ^.  receive  ? 

•'■':  -'     -   Ans.  3()00  pounds. 

11.  H.  has  1000  bushtils  of  salt,,  at'l  dollar  10  cents  per 
bushel ;  for  which  AV.  is  to  give  him  80  gallons  of  brand}'-, 
at  87-5  cci;its  per  gallon j" and  the  rest  in"  cotton,  at  15  cents 
per  pound.     How  many  pounds  of  cdttoti  mu^  II.  receive  ? 

Ansi'6866^  pounds. 

12.  Vv  iUit  quantity  of  jcandles,  at  S9  50  cents  })er  ewt., 
must  be  give^  for  locwt  Oqr.  27ij),  oi'  tobacco,  at  20  cents 
per  pound?  Ans.  ii5cwt.  oqr.  20ib.  4- 

.'I'j.- Two  pev.vJMi  '."'ai'vi-  -  A.  h.'i!;  J7cwt.  of  iroii;"a,t  13* 

cents  per  lb.  —  B.  ;has  12001b.  of  cheese,  at  14  dollars  per 

cwt. — which  of  tkem  muBif receive  money,  and  how  much? 

•'  Aufj.  A.  107  dollars  4  cental. 

li.  E.  has  2iOSib.  of  bacon,  at  10  cents  per  jx^und,  and 

'81  bushel'?!  of  applep,  ni  Tl^  'cents  per  bushel,  wliich  ho 

barters  with  P.  thus :  E.  to  luve  185  dollar.^  25  cents 'in 

money,  and  the  rest  in  pork,  at  1  dollar  58  cents  per  barrel. 

•How  many  barrels  it;  he  to  j-cwivc  ?        Airj.  50  barrels.  H- 

15.  K.  bought  of  y.  1021b.  of  lard,  at  8  J  ccnta  per 

pound,  and  is  to  pay  him  as  follows,  viz:  in  c;:.sh  1  dollar  1 

■cent,  20  lb.  of  leather,  at  20  ceul-s  per  pound,  and  40  pounds 


LOSS    AND    GAIN.  87 

of  Leef,  at  2  J  cents  per  pound,  and  the  rest  in  butter,  at  6] 
cents  per  pound.  How  many  pounds  of  Ijutter  must  Y 
receive  ?  Ans.  o9|^  pounds 


LOSS  AND  GAIN. 

Loss  and  gain  is  us^ed  to  sliow  bow  much  ia  gained  or  lost 
in  dealing. 

RULE. 

1st.  Subtract  the  cost  from  the  sale ;  the  remainder  will 
be  the  gain.  Or,  if  the  coat  be  more  than  the  sale,  pubtraot 
the  sale  from  the  cost;  and  the  remainder  will  lo  the  lo?s. 
2d.  Wlien  you  wish  to  sell  any  commodity  at  a  certain  gain 
per  cent.,  and  wish  to  know  what  sum  it  must  be  s<"'ld  for, 
say;  if  100  give  100  with  the  per  cent,  added,  what  will  the 
firr.t  cost  frive  ?  3d.  Wlieii  the  amount  is  ffivcn  at  a  certain 
rate  gain  per  cent.,  to  find  the  first  cost,  say;  if  100,  with 
the  rate  per  oeiit.  added,  give  lUO,  what  will  the  amourr. 
give?  4th.  When  any  commodity  is  Hold  at  n  certain  rate 
per  cent,  loss,  to  find  thk  sum  received,  say ;  if  ]  00  give  100 
less  the  per  cent,  lost,  what  will  the  first  cost  give  ? 

EXAMPLES. 

1.  What  will  a  merchant  gain  by  buying  95  bushels  of 
salt,  at  1  dollar  20  cents  per  bushel,  and  soiling  it  again,  at 
1  dollar  50  cents  per  bushel  ? 
$  cts. 

1  50  .95  bushels 

1  20  80 


Gain  on  one  bushel,  ^30'  x\ns.  $28  50  cents. 

2.  Bought  55  3'ardp  of  cloth,  at  13,  cents  per  yard,  and 

^old  the  same  again  for  15  cents  per  jnil-d.     How  much  ^im 

gained  by  the  tiarisaction 'r'  .      Ans.  $]   10  cts.  ■ 

'I      3.  If  1  buy  50  yards  of  clntir,  at  25  cent's  per  yard;  and  I 

soil  the  pamc  again  for  30  centiper  yard,  how  much  do  1  f 

•  •(.   If  1  buy  100  yards  of  tape,  ;.. 

si'1]  It  f(ir  TS  ecn ts  p"ryar(3,  ho»v^iut»vii;-«i;i  '  ilio  jj 

tn:ri^actioiV?  >                                                    Ai  .r^^.  i 

lU         ■  -' -,, , ,     ^-  ._„^, 


\SS  LO^JS    AND   GAIN. 

5.  If  I  buy  40  saddles,  at  11  dollars  50  cents  eacb,  aii<l 
sell  thciTi  ngiiin  at  10  dollars  99  cents;  how  much  do  I  lose 
by  the  sale "?  Ans.  20  dollars  40  cts. 

(j.  Bought  12  bushels  of  corn,  at  22^  cents  per  bushel, 
and  sold  it  again  at  22  cents  per  bushel.  How  much  did  T 
lose  by  the  transaction?  Ans.  G  cent:^. 

7.  A  man  bought  flour,  at  85  per  barrel,  and  sold  it  at 
$5  25  ccnt«  per  barrel.  How  much  did  he  gain  on  o^.o 
barrels  ?  Ans.  90  dollars  75  ets. 

8.  If  1  lay  out  500  dolhrs  in  cloth,  at  5  cents  per  yard, 
and  sell  the  same  again  at  12^  cents  per  yard,  how  nnich 
do  I  gain  ?  Ans.  750  dellars. 

9.  If  I  buy  a  horse  for  GO  dollars,  at  how  mueh  must  I 
sell  him  to  gain  20  per  cent.  ? 

If  100  :  60  :  :  120.     Ans  ?72. 

10.  If  I  buy  100  yards  of  cloth  for  §50,  at  how  nnieh 
must  I  sell  it  per  yard  to  gain  20  per  cent,  by  the  whole  ? 

Ans.  GO  cents. 

11.  If  I  buy  54  yards  of  muslin  for  29  dollars  84  cents, 
and  sell  the  same  again  at  60  cents  per  yard,  how  much  do 
I  gain?  Ans.  2  dollars  56  cents. 

12.  If  I  buy  90  horses  for  1800  dollars^  at  how  much 
must  I  sell  oach  horse  to  gain  180  dollars  in  the  whole  ? 

Ans.  22  dollars. 

13.*  A  merchant  sold  40  yards  of  cloth,  at  20  cents  per 

yard,  and  by  so  doing  gained  10  per  cent.     "What  was  the 

first  cost  of  each  yard  ?  Ans.  18  cents.  -|- 

40 

20 

110  :  800  :  :  100 
100 

11|0)8000|0 

Yards  4|0)72|7i 


18  + 


14.  B  )ught  a  quantity  of  tea  for  ?5250,  and  sold  it  for 
275  dollars.     What  is  the  gain,  and  gain  per  cent.? 

Ans.  25  dollars  gained,  10  per  cent,  i 


Fii  I  ■   1^   II     II  [111  II  111  II I II 1 1  II  Ml     I  jjxjjLJi  J  lUMiMiilMihilllrn iimimiaMMiil>iifW«i]<«ii«'.'««i«j!»iLnrtcil 

•        I'AllTNERSillP.  89 

15.  Bought.  190  buFhols  of  corn  for  326  dollars,  and  sold 
the  same  for  870  dollars  10  cents.  "What  was  the  profit  on 
each  bushel  ?  Ans.  9  cents 

16.  Bouirbt  a  parcel  of  goods  for  60  dollars,  and  sold  thf* 
same   iuiinediatid}''  for  90   dollars^  with  6  months'   crcdil 
IIow  juucli  ])er  cent,  per  annum  was  gained? 

Ans.  100  per  cent 

17.  "When  a  broker  receives  in  exchange  5  cents  per  do] 
lar  profit,  how  much  is  the  gain  per  ceut. "?  Ans.  $5 

18.  A  man  purchased  7  pieces  of  cloth,  at  ^13  75  centi? 
perpieSe;  but  finding  it  somewhat  damnged,  he  paid  S3  1"?^ 
'cents  per  piece  for  dyeing  it.     At  how  ranch  must  each  pio-^ 

bo  sold  to  gain  12  per  cent,  on  tUe  whole  ? 

•     '  Ans.  $18  90  ccn.^. 

10.   A  trader  bought  250  barrel.'*  of  flour,  at  S4  50  cents 

a  barrel..   lIow  must  he  sell  each  barrel  to  gai-n  100  dollars 

by  the  bargain  ?  Ans.  $-4  90  cenws. 

20.  If  I  purchtise  16  pieces  of  cloth  at  14  dollars  per 

I  piece,  and  sell  5  pieces  a-t  17  dollars  per  piece,  and  6  at  15 

d<ilhirs  per  piece,  what  must  I  sell  the  rest  at  per  piece  to 

I  gain  12  per  ce)it.  on  the  whole/'  Ans.  $15  17cts.  6m. 


rARTNERSlIIP. 

rartncrship  is  a  joint  interest  or  property,  the  union  of 
two  or  more  persons  in  the  same  trade,  by  which  rule,  per- 
son*? in  company  trading  together,  are  enabled  to  make  a 
just  division  of  the  gain  or  loa^i,  in  proportion  to  each  man's 
stock. 

When  the  respective  stocks  have  no  time^ —  ] 

i 

RULE.  I 

» 

Add  the  several  shares  together,  which  amount  is  thej 
first  term;  either  i>erson's  share,  the  2nd.;  the  whole  gnin  ov[ 
lo.ss,  the  3rd.  Proceed  by  the  Rule  of  Three.  2nd.  When ' 
the  respevtive  stocks  have  time,  multiply  each  man's  stock! 
by  its  tijiic.  Add  the  several  products  together,  which 
i amount  is  the  fu'st  term;  cither  i/a.r(icular  product^  t)n«  2iiiV  ; 
the  whole  gain  or  lo&s,  the  ord.     Proceed  as  befoi 

]^'lO()^.     Add  together  all  the  shares  of  g;iin  or  lobS. 


jHtC*  rAllTNER^HlP..  j 


j  LA.  B.  and  0.  made  a,  Htock.  A.  h.^h  m  giO,  B  ^iK), 
jO.  S40,  aud  by  trading,  tliey  gained  oG.  ddlarH.  Wiiiit  was 
I  each  man's  phare  of  the  gain  r 

A.  20 

B.  30 

C.  -10 


Amount.  90 

:  20  : 

:  oG. 

Ana. 

A.'HfiLaro    U8. 

90 

:  30  : 

:  a(>. 

Ans. 

B.'s  «hare  ^12. 

90 

40  : 

Aus. 

O.'f?  share  810. 

Proof.  ^36. 

2.  A.  and  B.  purchiib^ed  goods  worth  80  dollars;  of  which 
A.  piiys  80  dollars  and  E.  50  dol^a^s.  ^'hoy  gaiued  20  dol- 
lar.'^ ;  Tvliat  is  the  caiii  of  each  ? 

"     .  Ans.  A.  $7  50  cts.     B.  S12  50  ctH. 

3.  Three  merchants  trading  together  gained  ^-SOO.  A.'s 
stocli  was  $800;  E.'s  stock  ^700;  C.'s  stock  $500.  What 
way  each  man's  share  of  tUe  gain  ? 

.Ans.  A.'s  share  ^200;  B.'s  $175;  C.'s  3125. 

I     4.  xi  merchant  lj<)ir>g  deceased,  worth, IS 00  dollars,  is 

Ifcniid  to  owe  the  following  sums:  — To  A.  $1200;  to  B. 

i$500;  to  C.  (?700.     How  much  is  each  to  have,  iu  propor- 

tio!i  to  the  debt?      Ans.  A.  8900;  B.  $a75;  and  C.  S525. 

I      5.'  B.  C.  and  D,  uiado  a  stock,  by  which  they  gained  800 

jdoiiar.-i;  wdiuroof  B.'s  stock  wmi  4U0  doiiyijiS;  C/s  500  doi- 

I  lars ;  aud  D.'s  GOO  dollais.     I  demand  each  man's  share  of 

the  «;ai.a.  'Ans.  B. 's  $213^ ;  C/s  $2GG^ ;  D.'s  $820. 

G.  Three  drovers  pny  amona*  them  800  for  ])ae:ture,  into 

which  they  put  200  cattle.;  oX  which  A.  had  50;  B.  80; 

1  C.  7(^     1  would  know  how  much  each  had  to  pay? 

Ans..  A..  $15;  B.  $24;  C.  $21. 

7..  F^ir  menr  formed  a  capital  of  3200  dollars.     They 

gained  in  a  certain 'time  05G0  dollars.     A. 'a  stock  w:is  5G0 

doilarr>;   B.'s  1040  dollars;   C.'s  1200  dollars ;•  and  P.'s 

400  dollars.     What  did  each  gain  ? 

Am.  A.'9$UM;B.'s2132;  C.'s  2460;  and  D.'s  $820. 

■  8.  B.  C.  and  '"    traded  together;  B.  put  in  50  dollars 

for  four  jiLO'jtIiRr,   ')  J  j':  ''ollars  for  6  months;  and  D.  150 


TS^ 


doliura  for  S  iiiontljs.     They  gained  12G  dollars  80  cts.; 
v/li-tt  is  cacli  man's  t-Iiarc  of  tlic'gaiu? 
V      m. 

B.    50  >:  4^200 

0.  100x6     600 

'    D.  150x8  1200 

"^^     cff!.  S   cts. 


-i; 


2000  :    200:  :  126  80  ("12  68  B. 

2000  :  ■«  GOO  :  :  120  80     Ans.  IsS  0^  0. 
.    2000  :.1200  :  :  120  80  (76  08  D. 

9.  0.  P.  and  R.  traded  togetlier ;  0.  put  in  100  dollars  for 
2  luoutha,  P.  200  dollars  for  four  luontha,  jmd  K.  400  dol- 
lars for  5  moutbf^,  and  by  trading  together  they  gained  600 
j  dollars  50  cents.     Row  miich  is  each  man's  gain  in  propor- 
I  tion  to  his  stock  ?  LO.    40  dollars    3 ^  cents. 

I  .  Aus.  Tp.  160  dollars- 18 Scents. 

(_  R.  400  dollars  SS-^l-  cents. 
•  10.  A.  and  W.  made  a  stock ;  A.  put' in '500  dollars  for  G 
months,  and  W.  2000  dollars  for  8  months,,  and  by  trading 
they  gained  2600  dollars.  I  demand  crtch  man's  share  of 
the* gain  '^  ,        f  A.     410  dollars  52  cents  5m.  -i- 

j\.n^,  I  W.  2189  dollars  47  cents  8m.  + 
11.  S.  G.  and  Tv".  made  a. stock  for  12  months;  S.  put 
in  at  first  500  dollars,  and  two  rtionths  after  Tie  put  iij  40 
dollars  more  ;  G .  put  in  at  first  ^05  dollars  50  -cents,  and  at 
tho  end  of  ten  months  he  took  out  300  dollars;  W.  put  in 
at  first  600  dollars  25  cci^s,  and' 4  months  after  he  put  in 
100  dollars,  and  6  months  after  that  lie  put  in  50  dollars 
50  cents  more.  At  the  expiration  of  12  months  their  gain 
is  1800  dollars  50  cents;  what  is  each  man's-  share  of  the 
gain?  rs.    Si88  89ccnts2m. 

An3:^{Gv  ?602  S'4  cents  7m. 
,,jt-W,t,?aip  OQicents  Om. 


KX.CIUNG„Ji. 

4  far th ill:  ponnj;     7/ 

12  pence ; .  ;  Jiiilling 

20  shillings. . i  r.nund.     £ 


s. 


92 


tXCHANCE. 


TABLE, 


Showing  the  value  of  English  Money  in  Federal  Money 


N.    Hampshire, 

Mas.'^achupeits, 

Now  York   and 

South  ( 

I^arolina 

New      Jersey, 
Pennsvlvania, 

Rhode      Island, 

Connecticut, 
Virginia,    Ken- 

North Carolina. 

and  Georgia. 

Delaware,    and 

Maryland. 

tucky, and  Ten- 

nessee. 

S. 

d. 

^ 

els. 

s. 

d. 

^ 

c/s. 

5. 

d. 

$ 

c/s. 

s. 

d. 

$ 

cts. 

■ 

2  . 

0 

» 

2 

3. J 

o 

2 

2 

2f 

3 

3 

3 

5^ 

3 

H 

3 

4 

4 

4 

4 

7 

4 

H 

4 

5^ 

4^ 

4^ 

4^ 

Tof 

4^ 

5 

H 

6J 

6 

G| 

6 

6 

o§ 

6 

8i 

9 

9^ 

9 

IG 

9 

10 

9 

12^ 

1 

0 

12^ 

1 

0 

2U 

1 

0 

13^ 

1 

0 

IGf 

1 

6 

ISi- 

G 

32 

1 

G 

20 

1 

6 

25 

0 

0 

25 

2 

0 

42  f 

2 

0 

m 

2 

0 

33^ 

2 

28 

2 

48 

3 

30 

•3 

37^ 

2 

G 

31i 

o 

G 

53^ 

6 

33J 

G 

ill 

0 

9 

34^ 

9 

58f 

9 

361 

2 

9 

451 

3 

0 

37» 

o 
O 

0 

64  i 

3 

0 

40 

0 

50 

3 

t) 

4Gf 

9 

80^ 

9 

50 

9 

62^ 

4 

0 

50 

4 

0 

m 

4 

0 

53i^ 

4 

0 

m 

4 

6 

56  i 

G 

m 

4 

^ 

GO 

6 

75 

5 

0 

G2^ 

5 

0 

1 

7 

5 

0 

G6f 

5 

0 

83i 

610 

75 

6 

0 

1 

m 

6 

0 

80 

6 

0 

1 

00 

6 

9 

m 

G 

9 

1 

44^ 

9 

90 

9 

1 

12^ 

7 

G 

mi 

7i6 

1 

GO^ 

/ 

G 

1 

00      7 

6 

1 

25 

10 

6 

1 

m 

10 1  6 

'^ 

25 

10 

6 

1 

40     10 

G 

1 

75 

JYote.  In  calculating  the  above  table,  remainders  arc  not 
marked,  being  less  than  I,  &c. 

£1  of  New  York  and  North  Carolina,  is $2  50 

£1  of  South  Carolina  and  Georgia,  is $4  28  J  + 

£1  of  New  Jersey,  Pennsylvania,  Delaware, 

and  Maryland,  is . ; S2  6Gt 

£1  New  Hampshire,  Massachusetts,  Ehode 
Island,  Connecticut,  Virginia,  Kentucky, 
and  Tennessee,  is $3  33^  • 


: - 



— 

EXCHANGE. 

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-r  — 

94  EXCHANGE. 

A  TABLE  OF  OTHER  FOEEIGN  COINS,  &c., 

WITH  THEIR  VALUE  IN  FEDERAL  MONEY. 

$  cts.m.  cts.m. 


Poimd'  Sterling ....  4  44  4 
Pound  of  Ireland..  4  10  0 
Pagoda  of  India...  1  94  0 

j  Tale  of  Chma 1  48  0 

I  Millrca  of  Portugal.  1  24  0 
■i  Ruble  of  Eu^'sia...  0  CG  0 


The  Guilder  of  the  )    39  q 
United  Netherlands  ) 
Mark    lianco   of      "^    33  5 

Hamburg   .....  j 
Livre    Tournois   of  1    -j^^  ^^ 

i,xtuuic  ui  xiLi.Tox.. V-   V.W   ..   ,       rr;)nce ) 

];Pvupee  of  Bengal . .      55  5  |  Ilcid. Plate  of  Spain      10  0 

i  JS'oLe.  Some  persons,  to  try  others'  skill  in  numbers,  may 
'give  them  the  multiplyiDg  of  pound;:!,  {.hillings,  pence,  ka.y 
;  by  the  winie ;  or  the  multiplying  of  cents  by  the  same,  &c. 
The  following  will  be  sufficient,  thus: — Pounds  m\dtiplied 
by  pounds,  gTve  pounds,  l^ouhds  multiplied  by  sliiliings,  | 
give  shillings.  Shillings  multiplied  by  shillings,  give  the ' 
20th  part  of  a  shilling.  Shillings  multiplied  by  pence,  give 
the  20th  part  of  a  penny.  Pence  multiplied  by  pence,  give 
the  240th  part  of  ri' penny,  &c. ;  and  cen^•^  Tp.nltiplied  by 
cents,  give  the  100th  part  of  a  cent,  &c. 

EXCHANGE. 

Exchange  teaches  to  change  a  sum  of  one  kind  of  money 

to  a  given  denominaiion  Of  imother  kindj    to  reduce  the 

•  euiTcncy  01  each  (if  the  United  States  to  dolhu'S  and  cents, 

||  or  Federal  Money. 

'  HULL.  '  ! 

Ilcduco  the  sum  to  peace )  to  the  pence  ;iunex  two  ciphers ;  1 
then  divide  by  the  number  of  pence  which  make  a  dollar  in, 
that  state  or  country.     The  quotient  will  be  cents;  which] 
1  reduce  to  dollars.  1 


vYo/e.     This  rule  ..fipplie.-\to  the  currency  of  any  state  or,', 
I!  country,' if  its  cuiT(in<*l  be  in' pounds,  shillings,  pence,  o:c. 

i;XA3U'LLS. 

1.   Ill  UO  povLuds  .N.,'W  England,  Virginia,  Kentucky  andj 


I  EXCHANGE. 

I 


^h^i^r^'^r,!^'^''^'  ^""'^  "'''''^  '^''"^''  ''""^  centP,  a  dollar 


90 

is  00 
12 


s. 


I  '       72)21G0000(.S300  00 

I  21(3 

0000 

2    liring  12  pound.,  ^  sliiiiiiigs:  and  0  pence  to  dollar  J 
aud  cent,  sainc^cTurenoy.  a^3.  g^O  G2^  ct  J 

3.  Keduce  19  shillings  and  10  pence  to  dollars  and  cents  = 
same  cnrroncv.  ^     .  .  A,i^  «Rq  ^^n.f    >    ';• 

i    y     ^-,..t'  ,    ,  •  -^iife-  WO  Ducts.  5m. ! 

-4.  in   roo  pounds  how  many  dollars,  cents  and  mill,  : 
same  currency  r  W$2548  83cts.  in  :(. 

0    Keduce  S0£  and  Ss.  to  dollars  and  cents,  same  cm- 1 

c7't.  o^p  o     ^  ,„     .        Ans.  8100  50cte.l 

.nd  \V.fCr    i-      "'''  ^-^^^^^J  dollars  and  cent.,  New  York  ^ 
a.Kl  Aoxth  Oarohna  currency,  one  dollar  being  90  pence? 

- .   ill  oO£  how  many. dollars  and  cents,  same  currency? 
s    Tn  <)r  tr     1  ,„    •  Ans.  S75  00  ct«.' 

,e,;vf  '""'  "''"^'  ^^^^"^"-^  =^"'^  <^^"<^^  ^"me.  cur- 

I    ^'^    T,.  ^'Hr    r  V       r  r  '  Ann.  ,Sf^4  50  c(8. 

M-^rvl  nri'  >;'^  '       7  '^'''"'''  ^^''^"-^y^^^'^ia,  Delaware  and 

f'-k     T     tor-  T  -^vn^.  O-'OlL  {JO  ct:;. 

1^.  in  12£  how  many  dollars  and  ccuta,  same  currency? 

Jl.    I.i  8fi:<   Of<.  5(1.  how  miny  dollnrs,  een^s  and  rrll-  ' 
same  currcncv  ?  '         \  nt,  «oQn  i  o  ^     o  "'  I 

12.  Tn  5(U,  :-^::,uI,   (.':ir..lio:,  .ndOenmacm-rencv'how 
mamy  dollars  and  eent^,  bcin.  i>G  pence  in^  dollnr  ?  ^^ 

11     IS    T,  oiri  ,  n  ,        An::.  8240  00  cts. 

!  ""•  ^'*"y^>^'l'''»'--^'?»nd  cents,  same  currency? 

L-  ^ -  ,  '^J»s.  890  00  cts.  I, 


96  EXCHANGE. 

{     14.  In  460j£  and  16s.,  sterling  money,  liow  many  uollars 
and  cents,  being  54  pence  in  a  dollar?       Ans.  §2048  00  ets. 

To  bring  dollars,  or  dollars  and  cents,  to  pounds,  shil- 
lings, &c. 

RULE. 

Multiply  the  dollars,  or  dollars  and  cents,  by  the  number 
■  of  pence  'which  make  a  dollar  of  the  currency  into  which 
you  wish  to  bring  the  given  sum.      The  answer  will  be 
pence,  which  bring  to  pounds. 

JVo/e.  If  there  be  cents  in  the  given  sum,  two  figures 
must  be  cut  off  from  the  right  of  the  product,  before  bring- 
ing them  into  pounds,  &c.  - 

EXAMPLES. 

1.  In  33  dollars  how  many  pounds,  &c.  sterling,  a  dollar 
being  54  pence  ? 

S 

83 

54 


182 

165 

]2)1782d. 
210)14|8— 6d. 
Ans.  7£  8».  6d 

2.  1,000,000  dollars  how  many  pounds,  same  currency? 

Ans.  225,000£. 

o.  In  150  dollars  25  cents  how  ninny  pounds,  <tc..  New 

'■  Eiidand,  Virginia,   Kentucky  and  Tennessee  currency,  a  [ 

! dollar  being  72  pence?  Ans.  45£  Is.  6d. 

I      4.  In  2070  dollars.  New  Enghmd,  Virginia,  Kentucky 

and  Tennessee  currency,  how  many  pounds,  <ltc.,  a  dollar 

being  72  pence?  Ans.  ()21£. 

5.  In  24  dollars  50  cenis  how  many  pounds  and  shillings, 

&c.,  in  New  YorK  and  ^orth  Carolina  cnrroucy,  a  dollnr 

being  96  cents?  Ans.  0£  16s.  Od. 


VULGAll   I'RACTIONS  97 

6.  In  2512  dollars,  how  many  pounds  of  New  Jersey, 
Pennsylvania,  Delaware,  and  Maryland  currency,  a  dollar 
being  90  pence  ?  Ans.  942£. 

7.  In  90  dollars,  how  many  pounds  South  Carolina  and 
Georgia  currency,  a  doliai'  being  66  pence  ?  Ans.  21£. 

To  change  the  currency  of  one  state  or  country  into  that 
of  another. 

RULE. 

Place  the  sum  you  wish  to  change,  in  the  third  place  — 
the  number  of  shillings  in  a  dollar  of  that  currency  into 
which  you  wish  to  change  it,  in  the  second  —  and  the  num- 
ber of  shillings  in  a  dollar  of  that  currency  you  wish  to 
change,  in  the  first.     Proceed  by  the  Kule  of  Three. 

1.  What  is  the  value  of  60£  Tennessee  currency,  in  New 
York  ? 

S.    S.      £. 

6  :  8  :  ;  50 

8 

6)400 

Ans.  66£.  13s.  4d. 

2.  What  is  the  value  of  500£  Massachusetta  currency, 
in  Pennsylvania?  Ans.  625£. 

3.  What  is  the  value  of  100£  South  Carolina  or  Georgia 
currency,  in  Kentucky?  Ans.  128£.  lis.  5d.-{- 

4.  What  is  the  value  of  750£  New  Hampshire  currency, 
in  North  Carolina?  Ans.  1000<£. 


VULGAR  FRACTIONS. 

A  Vulgar  Fraction  is  a  part  of  a  whole  number,  and  is 
read  by  first  mentioning  the  upper  part  of  the  fraction,  and 
then^  the^  lower,  thus :  i,  |,  &c.  The  upper  part  of  the 
fraction  is  called  the  numerator,  and  shows  the  part  o(  a 
whole  number  expressed  by  the  fraction.  The  lower  num- 
ber is  called  the  denominator,  and  shows  the  number  of 
such  pai'ta  contained  in  a  whole  number.  Vulgar  Fractions 
ai'c  either  proper,  improper,  compound,  or  roixeS.     A  proper 


98  vulgXh  tractions. 

fraction  lias  its  numerator  less  than  its  denominator,  m  |,  |, 
&c.  An  improper  fraction  has  its  numerator  greater  than 
its  denominator,  as  f,  *,  &c.  A  compound  fraction  is  a 
fraction  of  a  fraction,  with  the  word  "  of  ^'  expressed  between 
them,  as  J  of  s,  of  |,  &o.  A  mixed  number  b  a  whole 
number  and  a  fraction,  as  5i,  81,  &o.        ,a^.  ,,-. 


REDUCTION  OF  TULCtAR  FRACTIONS. 

CASE   1. 

To  reduce  a  fraction  to  its  lowest  terii». 

Di^'ide  the  numerator  and  denominator  continually  by 
j  an  J  number  that  will  divide  them  both  without  a  remainder. 
i  When  they  cannot  be  divided  by  any  number  without  a  re- 
j  mainder,  the  fraction  is  then  at  its  lowest  terms. 

EXAMPLES. 

1.  Reduce  |f  to  its  lowest  terms; 

24)11=  ^Ans. 

2.  Reduce  ai  to  its  lowest  terms.  Ans.  ^. 

3.  Reduce  {|  to  its  lowest  terms.  Ans.  J. 

4.  Reduce  j  f  |  to  its  lowest  tenne.  Ans.  f . 
6.  Reduce  /g%.  to  its  lowest  terms.  Ans.  ^. 
6.  Reduce  ||f  to  its  lowest  tcn»9.  Ans.  -fj. 

CA«E  2. 

To  reduce  a  mixed  number  to  an  improper  fractioB. 

RULE. 

Multiply  the  whole  number  by  the  denominator  of^the 
fraction,  and  add  the  numerator  to  the  product  for  a  new| 
numerator,  uuder  which  place  the  given  denominator. 

EXAMPLES. 

1.  Reduce  11|  to  an  imi>roper  fraction.  Ane.  Y- 

New  numerator.  57 
Denominator.        5 


VULGAR  I'HAOTIONS.  99 

2.  Reduce  8^  to  an  improper  fraction.  Ana.      Y- 

3.  Reduce  14  J  to  an  improper  fraction.  Ans.       V- 

4.  Reduce  99|?j-  to  an  improper  fraction.        Ans.  'f|^. 

CASE  3. 

To  reduce  an  improper  fraction  to  a  whole  or  mixed 
number. 

EULE. 

Divide  the  numerator  by  the  denominator. 

EXAMPLES. 

1.  Reduce  \y*  to  its  prop^*  terms. 

17)400(An3.  23A. 
J  34' 

"60 
51  ' 

9 

2.  Reduce  ^y  to  its  proper  terms.  •  Ans.  22 1 

3.  Reduce  J  i  to  its  proper  terms.  Ans.  5j'^ 

4.  Reduce '*^/;i^  to  its  proper  terms.  Ans.  2^j 

JVbte.    Case  2d.  and"  3rd.  prove  each  other. 

CASE  4. 

To  reduce  compound  fractions  to  single  ones. 

RULE. 

,  Multiply  all  the  numerators  together  for  a  new  numerator, 
and  all  the  denominators  for  a  new  denominator;  "which 
reduce  to  their  lowest  terms. 

EXAMPLES. 

1.  Reduce  J  of  §  of  J  oj  a  to  a  single  fraction.     Ans.  J. 

1x2x3x4=  24  = 

24) (J. 

2  +  3x4x5=  120 


100  VULGAR  FRACTIONS, 

2.  Reduce  ^  of  |  of  f  to  a  single  frnction.  Ane.    f . 

8.  Reduce  |  of  |  of  ^  to  a  single  fraction.  Ans.  -^. 

4.  Reduce  |f  of  |  of  J  to  a  single  fraction.       Ans.  y\. 

CASE  5. 

To  find  a  common  denominator,  viz :  one  whose  denomi- 
nators are  all  alike. 

RULE. 

Multiply  all  the  denominators  together  for  a  common 
denominator,  into  which  divide  each  denominator,  and  mul- 
tiply the  quotient  by  its  own  numerator  for  a  new  nume- 
rator, and  place  the  new  numerator  over  the  common  de- 
nominator. 


EXAMPLES. 

1.  Reduce  J,  f  and  f  to  a  common  denominator.     . 

iff     12  X  1  =     12 

3       8x2=     16  new  numerators. 
—      6x3=     18 
12 

2 

—  m 

Divide  hy  2,  8,  4.  24  common  denominator. 

Ans.  2  4?  2*;  'if' 

2.  Reduce  J,  |  and  ^  to  a  common  denominator. 

At1<5     2.1     11     56 

3.  Reduce  |,  |,  |,  -f ,  to  a  common  denominator. 

Anq   :!^-^   l^^   ^^^    ^*-5- 

4.  Reduce  J,  §,  |-  and  |,  to  a  common  denominator. 

An<?    I"!     15.2     210     25.2 
xxua.  .rtis)  2  8  8>  asaJ  28  8* 

CASE  6. 

To  reduce  the  fraction  of  one  denomination  to  the  fraction 
of  another,  but  greater,  retaining  the  same  value. 

RULE. 

Make  the  fraction  a  cf^mpound  one,  by  comparing  it  with 
all  the  denominations  between  it  and  that  to  which  it  is  to 
be  reduced;  which  fraction  reduce  to  a  single  on6. 


VULGAR  FRACTIONS.  101 

EXAMPLES. 

1.  Ilcdiicc  I  of  a  pennyweight  to  the  fractioifof  a  pound, 
Troy. 

2.  Reduce  |  of  a  nail  to  the  fraction  of  a  yard. 

Ans.  y|j  yd. 

3.  Reduce  f  of  a  cent  to  the  fraction  of  a  dollar. 

Ans.  yl^  dollar. 

4.  Reduce  |  of  a  pint  to  the  fraction  of  a  hogshead. 

Ans.  -^-^^  hhd. 
CASE   7. 

To  reduce  the  fraction  of  one  denomination  to  the  fraction 
of  another,  but  less,  retaining  the  same  value. 

RULE. 

jNTultiply  the  given  numerator  by  the  parts  of  the  deno- 
miiintor  between  it  and  that  to  which  it  is  reduced,  for  a 
new  imnicrator,  and  place  it  over  the  given  denominator, 
which  reduce  to  its  lowest  terms. 

EXAMPLES. 

1.  Reduce  -^^^  of  a  dollar  to  the  fraction  of  a  cent. 

Ans.  f  cent. 
els. 

_1        y     100  —  9IO^>C|iL  —  1 

2.  Reduce  ^j  of  a  pound,  troy,  to  the  fraction  of  an 
ounce.  Ans.  f  oz. 

3.  Reduce  ^^^  of  a  cwt.  to  the  fraction  of  a  pound, 
avoirdupois.  Ans.  ^  lb. 

4.  Reduce  y^y^  of  a  day  to  the  fraction  of  a  minute. 

Ans.  j^  min. 

CASE   8. 

To  reduce  a  fraction  to  its  proper  value. 

^,  RULE. 

^Multiply  the  numerator  by  the  next  lowest  denomination, 
and  xlivide  by  the  denominator. 

"  n  ■■■■       "^ "r-T— TTT-u-TTTTT- 


*  t         ■        ■  '  T^— '  ■ 

102  VULGAR  FRACTIONS. 

EXAMPLES, 

1.  Itediige  J  of  a  dollar  to  its  proper  value. 

i 
300 

5)400 

Ana.  80  ccuta. 

2.  Reduce  f  of  a  dollar  to  its  proper  value. 

Ans.  75  cents. 

3.  Keduce  |  of  a  day  to  its  projSer  quantity. 

Ans.  6  hours. 

4.  Keiluce  |  of  a  mile  to  its  proper  quantity. 

*'  -^^'  Ans.  4fur.  125yd.  2ft.  lin.  •;. 

5.  Reduce  /^  of  an  acre  to  its  proper  quantity. 

Ans.  IR.  lOr. 

6.  Reduce  -j^q  of  a  year  to  its  proj^cr  quantity. 

Ans.  a28aa.  12Lr. 

CAKE  9. 

To  reduce  any  given  value,  or  quantity,  to  a  fraction  of 
any  greater  denomination  of  the  same  kind. 

RULE. 

Reduce  the  given  sum  to  the  lowest  denomiaation  men- 
tioned for  a  numerator,  and  the  denomination  of  which  you 
vnah  to  make  it  a  fraction  to  the  same  name  for  a  denomi- 
nator. 

EXAMPLES. 

1.  Reduce  60  cents  to  the  fraction  of  a  dollar. 

Ans.  ^  dollar. 
2t0)/vij  =  f 

2.  Reduce  90  cents  to  the  fraction  of  a  doWar. 

Ans.  -/^  dollar. 

3.  Reduce  9  ounces,  troy,  to  the  fraction  of  a  pound. 

Ans.  f  lb. 

4.  Reduce  9oz.  Sdr.  |,  avoirdupois,  to  the  fraction  of  a 
pound.  "'  Ans.  4  lb. 

5.  Reduce  8qr.  3na.  to  the  fraction  of  a  y'c^rd.     Ans.  if. 

6.  Reduce  7  months  to  the  fraction  of  a  year. 

Ans.  /j  year. 


VULGAR   FRACTIONS.  103 

ADDITION  OF  VULGAR  FRACTIONS. 

RULE. 

Reduce  the  fractions  to  a  common  dnnominator;  then  add 
all  the  numeratora  together,  and  place  their  sum  over  the 
common  denominator.  If  fractions  be  of  different  denomi- 
nations, i5nd  their  value  separately,  and  add  as  in  Compound 
Addition. 

Note.  If  mixed  numbers  be  given,  reduce  them  to  im- 
proper fractions,  or  only  use  the  fractional  part  in  perform- 
ing the  operation.  Then  add  the  whole  numbers,  as  in 
Simple  Addition.     If  compound  fractions  be  given,  reduce 


Ans.  I. 


Divide  by  8,  2,  4)64 

2.  Add  %,  and  y'^,  together.  Ana.  ^,''^. 

3.  Add  £,  I-,  fj^,  and  t,  together.  Ans.  y/^?^. 

4.  Add  j\j  /^,  -j^fj  and  y-^p  together.  Ans.  j^. 

5.  Add  j,  ^,  and  f,  togetner.  Ans.  Ij. 

6.  Add  3},  8f,  and  ^,  together.  Ans.  11 1;,^^. 

7.  Add  T^,  and  5},  together,  Ans.  13/^. 

8.  Add  i  of  an  acre  to  -^\  of  a  rood.  Ans.  2R.  10. 

9.  Add  f  of  a  mile  to  j\  of  a  furlong.  Ans.  6fur.  28P. 

10.  Add  3  of  ^  and  ^  of  J^  together.  Ans.  f  *. 

11.  Add  i  of  1  and  I  bf  is  together.  Ans.  ff 


them  to  single  ones. 

EXAMPLES. 

1.  Add  J,  if,  and  ^,  together. 

i  J   \ 
2 

8 
32 

8 

16 

8 

fl 

MULTIPLICiTION  OP  l^LGAR  FRACTIONS. 

\ULE. 

Multiply  lie  ^rsrirttcci  'ADgethcr  for  a  jew  numerator, 
and  the  deao«i»<iOfi  fo/i  i   aeii  (iionomin»tor. 


104  VULGAR  FRACTIONS. 

J^ote.  If  compound  fractions  be  given,  reduce  them  to 
single  ones ;  or,  if  mixed  numbers;  rgduce  them  to  improper 
fractions;  and  proceed  as  before. 

EXAMPLES. 

1.  Multiply  i  by  t,  i  X  t=f  2)|.  Ana.  h 

2.  Multiply  i  by  |.  Ans.  f^. 

3.  Multiply  Vv  by  h  Ans.  ^j, 

4.  Multiply  4|  by  |.  Ans.  8*. 

5.  Multiply  J  of  f  by  j\  of  jj.  Ans.  /j^. 

6.  Multiply  J  of  7  by  i.  Ans.  If. 
}XiXj=f        4)7 

1^ 


SUBTRACTION  OF  VULGAE  FRACTIONS. 

RULE. 

Reduce  compound  fractions  to  single  ones,  and  mixed 
niimbers  to  improper  fractions.  Then  reduce  these  frac- 
tions to  a  common  denominator,  and  subtract  the  less 
numerator  from  the  greater,  and  place  the  difference  over 
the  common  denominator. 

JS'ote.  When  the  fractions  are  of  different  denominations, 
reduce  them  to  their  proper  value,  each  separately,  and  take 
their  difference  by  Compound  Subtraction. 

EXAMPLES. 

1.  From  I  take  /  Ans.  ^\, 

8        12x5=60 
8X6=40 


Divideby8,12)9G 


4)if=A. 


2.  From  |-  take  |  .      Ans.  J,. 

3.  From  ^^  take  -^^.  Ans.  f . 

4.  From  y^^  take  A.  Ans.  ^\. 

5.  From  ^  of  |  take  |  of  f .  Ans.  i. 
G.  From  f  of  ^\  take  \  of  |.  Ans.  ^. 
7.  From  J  of  a  league  take  f^  of  a  mile. 

Ans.  Im-  2fur.  16p. 
— —^——^————————^'^ 


VULGAR  TRACTIONS.  106 

8.  From  ^  of  a  yard  take  ^  of  an  inch.  Ans.  5}  in 

JVote.  When  fractions  or  mixed  niimLcrs  are  to  be  sub- 
tracted from  whole  numbers,  subtract  the  numerator  of  the 
Iraction  from  its  denominator,  and  under  the  remainder 
place  the  denominator;  then  carry  t)nc,  to  be  subtracted 
from  the  whole  number. 

9.  From  5  take  /^.  Ans.  4-j-\. 


Ang.  9-f\. 

Ans.  3^. 

Ans.  -1. 


DIVISION  OF  VULGAR  FRACTIONS. 

RULE. 

Reduce  compound  fractions  to  single  ones,  and  mixed 
numbers  to  improper  fractions.  Then  invert  the  dividing 
term,  and  multiply  all  the  numerators  into  each  other  for  a 

dividend,  and  denominators  for  a  divisor. 

« 

EXAMPLES. 

1.  Divide  |  by  f .  Ans.  i 

inverted  f  X  h     2)^  =  |. 

2.  Div*  -    "  • 

3.  Div 

4.  Div 


5 

8 
1  4 

1.. 

8 

4 

tV 

10. 

From  10  take  J5, 

11. 

From  9  take  5^. 

12. 

From  25  take  24f^. 

5.  Div 

6.  Div 

7.  Div 

8.  Div 
0.-  Div 


de  (>  by  J.  Ans.  48. 

de  {i  by  3.  Ans.  -r-'^. 

de  H  by  §.  Ans.  l|f 

de  ^  by  i.  Ans.  19f 

de  I  of  i  by  ^  of  f  Ans.  %^}. 

de  f  of  .}  by  ^  of  f  Ans.  1^. 

de  ^of  iby|  of  ^.  Ans.  16^ 

de4iby5.of4.  Ans.  2^V 

10.  What  part  of  335V  is  28 jj?  A^s."!. 


RULE  OF  THREE,  IN  VULGAR  FRACTIONS. 

RULE. 

State  as  in  whole  numbers.     Then  invert  the  first  term, 
and   multiply  all  the  numerators  together  for  a  dividend, 


106  VULGAR   FRACTIONS. 

and  denominators  for  a  divisor.  If  mixed  numbers  be  given, 
reduce  them  to  improper  fractions ;  or  compound  fractions 
to  single  ones.     If  a  whole  number,  place  it  thus:  |-,  J,  &c. 

EXAMPLES. 

1.  If  f  of  a  yard  of  cloth  cost  f  of  a  dollar,  how  much 
will  f  of  a  yard  cost  at  that  rate  ?  Ana.  $1  60  cts. 

Inverted  f  X  ix  f  X  510)810 

^1  60  cts. 

2.  If  f  of  an  ounce  of  indigo  cost  J  of  a  dollar,  how  much 
will  I  of  an  ounce  cost?  Ans.  23-^^  cts. 

3.  If  If  bushels  of  corn  cost  $1J,  how  much  will  60 
bushels  cost  at  that  rate  ?  Ans.  $38  57|  ets. 

4.  If  2i  bushels  oats  cost  50  cents,  what  cost  13  J  bushels 
at  that  rate?  Ans.  $2  65  cts. 

5.  How  many  yards  of  linen,  ^  widS,  will  be  sufficient 
to  line  20  yards  of  baize,  that  is  f  of  a  yard  wide  ? 

Ans.  12  yd. 

6.  If  ^  of  a  pound  of  cinnamon  bring  f  of  a  dollar,  what 
will  If  lb.  come  to?  Ans.  $2  74f  cts. 

7.  What  will  i  of  2i.cwt.  of  chocolate  come  to,  when 
6  J  lb.  cost  f  of  a  dollar?  Ans.  $10  76||  cts. 

8.  When  10  men  can  finish  a  piece  of  work  in  20f  days, 
in  how  many  days  can  6  men  do  the  same  ?         Ans.  34^  da. 

9.  How  many  pieces  of  stuff,  at  $20  J  per. piece,  are  equal 
in  value  to  240A  pieces,  at  $12  J  per  piece  ?      Ans.  149^/-!^. 

10.  If  ^  of  #  of  f  of  60  cents  will  pay  for  a  bushel  of 
potatoes,  how  many  bushel  will  $1  60  cts.  pay  for  ? 

Ans.  lOjbu. 


DOUBLif  RULE  OF  THREE  IN  VULGAR 
•  FRACTIONS. 


RULE. 


Prepare  the  terms,  if  necessary,  by  Reduction.     State  as 
in  wlioie  numl.iers.     Then  invert  the  two  dividing  terms, 
and  multi[>ly  all  numerators  together  for  a  dividend,  and  the 
l|denominators  for  a  divisor. 


DECIMAL  TRACTIONS.  107 


EXAMPLES. 

1.  If  i  of  a  dollar,  in  /.^  of  a  year,  gain  ^.  of  a  dollar 
interest,  how  mueli  will  I  o{  a  dollar  gain  in  ^'of  a  year  ? 

Ana.  05  ct«. 
8    y.       8 
Principal.  *  :  /^  '  -  jV  lufeerest. 
I  :f 
Inverted  J  X  V  x  |  X  f  X  ^3  =  108|00)(>00l00=5§. 

MO 

.60 

2.  If  21  yards  of  cloth,  If  yards  wide,  cost  ^3j,  what  is 
the  value  of  38  i  yards,  2  y^ds  wide  ?        Ans.  itO  50  cts. 

3.  If  $50  in  i^^  months  gain  2^  dollars  interest,  in  what 
time  will  $15 J  gain  m  ?  Ans.  12if  J  months. 

4.  If  4  men  in  5|  days  cat  7j  lb.  of  bread,  how  many 
poiuids  will  20 'men  eat  in  |  of  a  day?  Ans.  5-"^  lb. 

5.  If  90  dollars  in  |  of  a  year  gain  $4i  interest,  in  what 
time  will  900  dollars  gain  20  dollars  interest  ? 

Ans.  4:^j  months. 


DECIMAL  FRACTIONS. 

A  Decimal  Fraction  is  a  part  of  a  whole  number  or  unit, 
denoted  by  a  point  placed  to  the  left  of  a  figure  or  fipires ; 
us  .2,  .18,  .110.  The  first  figure  after  the  point  denotes  so 
many  tenths  of  a  unit;  the  second,  so  many  hundredths; 
the  third,  so  many  thousandths ;  and  ho  on. 

Decimal  Fractions  are  read  in  the  same  manner  as  vulf'ar 
fractions.  .5  is  equal  to,  and  reads  as  j%  .10  j-^^,  .120  j'^'^'^^, 
{and  so  on.  A  mixed  number  consisting  of  a  whole  num- 
ber and  a  decimal,  as  Di/', ;  thus  12.5.  Whole  numbers, 
counting  fiom"  the  right  towards  the  left,  increase  in  a  ten- 
fold proportion  ;  but  detumale,  countina  from,  the  left  towards 
the  right,  decreajse  m  &  tenfold  proportion,  as  will  bo  better 
(Exemplified  in  the  fWIowing  iahh  : 


108  DECIMAL  TRACTIONS. 

TABLE.  ' 

;i^  ;r;  ;^  ;=;  ^  H  W  H  U?      h  >-i  h  r-<  th  S  rn  ,-^  rH 
222  2  22221        122222222 

Whole  numbers.  Decimals. 

J^ote.  Ciphers  annexed  to  decimals,  neither  ii)  crease  or 
decrease  them;  thus,  .4,  .10,  .50,  being  y\j,  rf^%  ^y^,  are  of 
the  same  value ;  but  ciphers  prefixed  to  decimals,  decrease 
them  in  a  tenfold  proportion;  thus,  .04,  .010,  .050,  being 

T^5>   i  ioT57  iooo?  ^'^' 


1 


ADDITION  OF  DECIMALS.  ' 

RULE. 

Wriic  down  the  given  nunibers  under  each  other,  viz,  : — 
j  Units  under  units,  tens  under  tens,  &c.,  and  add  as  in  addi- 
i  tion  of  Tvhole  numbers ;  observing  to  set  the  point  in  the 
answer  under  those  of  the  given  number. 

EXAMPLES. 

(2.)  30:12  (3.)  .7324 

3.112  .0962 

.12  .132 

16.182  •  .09 


18.078  55.534  1.0500 

4.  Add  56.12,  .7,  1.314,  5837.01,  and  .15,  together. 

Ans.  5895.294. 

5.  Add  361.04,  .120,  78.0006,  101.54,  8.943,  and"  .3, 

together.  Ans.  5 19.9436.  j 


DECIMAL  niACTlONS.  109  ( 

MULTIPLICATION  OF  DECIMALS. 

RULE. 

Multiply  as  in  whole  numbGrs,  and  point  off  as  many 
figures  in  the  product  for  decimals  as  there  are  decimals  in 
both  factors.  If  there  are  not  so  many  figures  in  the  pro- 
duct as  there  are  decimal  figures  in  both  factors,  place 
ciphers  to  the  left  of  the  product  to  supply  the  deficiency. 

EXAMPLES. 

1.  Multiply  5.11  by  .122 
6.11 


122 
122 
610 

.62342 


2.  Multiply  54.20  by  38.63.  Ans.  2093.7460. 

3.  Multiply  4560.  by  .3720.  Ans.  1696.3200. 

4.  Multiply  .285  by  .003.  Ans.  .000855. 

5.  Multiply  3.92  by  196.  Ans.  768.82 

6.  Multiply  .28043  by  .0005.  Ans.  .000140215, 


SUBTRACTION  OF  DECIMALS. 

Place  the  numbers  aa  in  addition,  with  the  less  under  the 
greater;  and  subtract  as  in  whole  numbers,  setting  the  point 
in  the  answer  under  those  in  the  given  numbers. 

EXAMPLES. 

1.  From  32.456  <ake  1.83 
1.33 


Ans.  31.126 
2.  From  18.16  take  9.125."  Ans.  9.035 

3    Frcm  100  take  25.  Ana.  99.75 


flTO  DECIMAL   FRACTIONS. 

4.  From  441.2  talie  128.9  Ans.  812.3. 

5.  From  456.1  take  tll.Q  Am 


■  ■■<  tma^m.  — *«iXw<wMB<**Mi 


3-14.2, 


DIVISION  OF  DECIMALS. 


EXILE. 

Divide  as  in  whole  numbers;  then  observe  how  many 
1  more  decimal  figiirea  tllere  are  in  the  cli\idend  than  divisor,. 
[  and  point  off  that  num])cr  of  decimal  figures  ia  the  answer. 

Or  if  there  be  not  figureB  enough  in  the  answer,  annex 

ciphers  until  there  be  a  sufficient  nmnber. 

JVb^e.  If  tiie  diA^dend  be  not  lai'gc  enough  to  eontain  the 
divisor,  annex  ciphera  until  it  will  be  >  or  if  there  be  a.  re- 
j  mainder,  proceed  in  like  manner. 

EXAMPLES. 

1.  Divide  148.63  by  4.21 

4.2lVl48.(>3(Ans.  '6bMi^ 
126.3 


n 


105 


128.0 

126.S 

16.84 
160 

2.  Divide  19.25  by  88.5  *               Ana.  .5. 

8.  Divide  .2142  by  iJ.2  Ane.  .066.  + 

4.  Divide  210.  by  240.  Ajis.  .875. 

5.  Divide  .1606  by  4.4  Ans.  ,865. 

6.  Divide  3.  by  4."  Ans.  .75. 

7.  Divide  275.  bv  3842.  Ana.  .OTIS'/'?,  -f 


fcdB».'  ■"iJftl*-3 


M»  «  rri-TiitwMWMM  I  .    l»«Mp—  ■■!    mi I  iiiiii  iiMaii  ij  i   imn   1 1  ■  1 1  ■■—— ■aaa— B— aai 

DECIMAL  rs ACTIONS.  Ill 

REDUCTION  OF  DECIMALS. 

CARE   1. 

To  reduce  n  vulgar  frnctlpn  to  a  decimal. 

1 

;  i\jinex  ciphers  to  the  numerator,  and  divide  by  the  de- 
nominator. If  compound  fractions  be  giTCD,  reduce  them 
to  single  ones,  and  then  to  a  decimal. 

EXAMPLES. 

1.  Heduce  |  to  a  d«^cimal.         ^  Ans.  .5. 

55)1.0 

5 

2.  Reduce  J  to  a  decimal.  Ans.  .333 

3.  Reduce  f  to  a  decimal.  Ans.  .75 

4.  Reduce  f  to  a  decimal.  Ans.  .375. 

5.  Reduce  ^  of  f  to  a  decimal.  Ans.  .333.  -4- 

CASE  2. 
To  reduce  any  sum  or  quantity  to  the  decimal  of  a  higher.  | 

RULE. 

Reduce  the  ^ven  sum  to  the  loweat  denomination  men- 
tioned for  a  dividend,  and  one  of  tliat  denomination  of  which 
you  wish  to  make  a  decimal  to  the  same  denomination  for  a 
divisor.     The  quotient  will  be  the  answer. 

EXAMPLES. 

1.  Reduce  Sqr.  to  the  decimal  of  a  yard.  Ans   ,5 

vd. 
1  4)20 

5 

4 

2.  Reduce  2qr.  2ua.  to  the  decimal  of  a  yard. 

Ans.  .625. 

3.  Reduw  2qt.  Ipt.  io  the  decimal  of  a  hhd. 

Ans.  .00992  +. 


as 


112  DECIMAL   FRACTIONS. 

4.  Reduce  lOgr.  to  the  decimal  of  an  onnce,  apotliccaries' 
weight.  Ans.  .02083.  + 

5.  Reduce  5  minutes  to  the  decimal  of  an  hour. 

Ans.  .08*333.  -f 

6.  Reduce  2r.  4p.  to  the  decimal  of  an  acre.    Ans.  .525. 

CASE  3. 
To  reduce  a  decimal  fraction  to  its  proper  value. 

RULE. 

Multiply  the  given  fraction  continually  by  the  next  lowest 
denomination  than  that  of  the  given  sum,  for  the  proper 

value. 

EXAMPLES. 

1.  What  is  the  value  of  .75  of  a  doUai-?         Aur.  TGcts. 

100 


75.00 

2.  What  is  the  value  of  .375  of  a  dollar?     Ans.  37^cts. 

3.  "What  is  the  value  of  .9  of  an  acre  ?        Ans.  3r.  23p. 

4.  What  is  the  value  of  .436  of  a  yard  ? 

Ans.  Iqr.  2na.  .976. 

5.  What  is  the  value  of  .71  of  4  ounces,  troy  ?   , 

Ans.  2oz.  lOdwt.  19.2gr. 

6.  What  is  the  value  of  .86  of  cwt.  ? 

Ans.  3qr.  121b.  5oz.  1.92dr. 

7.  What  is  the  value  of  .07  of  a  ban-el  of  32  gallons  ? 

Ans.  2gal.  1.92pt. 

8.  W^hat  is  the  value  of  .235  of  a  day  ? 

Ans.  5hr.  38min.  24sec. 


RULE  OF  THREE  IN  DECIMALS. 

EULE.  ^ 

State  as  in  whole  numbers,  only  observing  when  you 
multiply  and  divide,  to  place  the  decimal  points  according 
lo  the  rules  of  multiplication  and  division  of  decimals. 


involution;  dRji. iiAibiNQ  of  rOWERS.  "'"113 


EXAMPLES. 

1.  If  G.-l  lb.  of  coffee  cost  l-'22  dollars^  what  cost  25.6  lb. 
6.4  :  25.6  :  :  1.22  ?  ^  Ans.  U  88  ceut.s.  M 

2.  If  1.4  lb.  of  sugar  cost  .10  of  a  dollar,  witat  will  SOcwt. 
Iqr.  22.5  lb.  come  to?  Ans.  $389.77Lh- 

3.  If  I  sell  Iqr.  of  cloth  for  §2.345,  wliat  ir,  it  per  vard  ? 

Ana.  i9M. 

4.  Iiow  many  pieces  of  cloth  at  $20.8  per  jsiece  ai'e  equal 
in  value  to  240  pieces  at  $12.6  per  piece*/ 

Ans.  145.38.  -\- 

5.  How  loiag  will  3  nieii  be  ia  performing  a  piece  of 
work  which  will  occupy  5  nien  for  40.5  days? 

Ans.  G7.5  days. 
Ifuw  luuch  niusiin  .75  of  a  yard  wide  will  line  25.5 


6. 

yardi' 


of  c]ulJi  that  is  5  l!^uartcrs  wide  ? 


Ans.  42.5  yards. 


INVOLUTION;  OR,  RAISING  OF 
POWERS, 

A  power  is  the  product  produced   by  multiplying   any 
giveu  number  iuto  it,self  a  certain  niunber  of  times. 

Thus,  3  X  8=::  9,  the  square  or  second  power. 
SxSx  8=27,  the  cube  or  third  power  of  3. 
3  X  3  X  3  X  3  X  =81,  the  fourth  power  of  three,  &c 

The  number  which  denotes  a  power  is  called  its  index. 
Any  nuiubei  multiplied  by  the  same  sum  one  timo,  the  pro- 
duct is  its  square.  Thus,  2  by  x2  =  4,  the  square  of  2^ 
SiQ...  Any  number  multiplied  into  its  square,  the  product 
will  be  the  cube.  Thus,  2x2  X  2- 8,  the  .cube  of  2.  When 
'  any  power  of  a  \T.ilgar  fraction  is  nnpiirod,  first  raise  tlie 
numerator  to  the  required  power  for  a  now  numerator,  and 
thea^ajijSe  the  denominator  to  1  he  required  power  for'Aiiew 
4<}U9*Riaa.toA\     Tl^jfis,  A|je  ihird  pow^f  of  |  x  f  x  t~. 

c;-  ^  Ans.  .^^  ^^^  required  powf^re,  , 


^■^Ej 


==1 


IM 


^QTjAliE    HOOT, 


TABLE  OF  THE  FIE8T  NINE  PO\VeKS. 


t^ 

rfJ 

o 

>;». 

tri 

a> 

-J 

(/: 

CO 

^ 

^ 

c 

c 

ts' 

ft- 

B- 

(-♦ 

cr 

ir 

^ 

?f5 

5^ 

o 

? 

? 

? 

? 

OE 

^ 

^ 

:5 

^, 

^ 

^. 

flj 

CD 

ct 

o 

o 

CD               ( 

1 

"i 

• 

Jl 

't 

r« 

p 

r'             ] 

1 

1 

1                    1 

1 

1 

li 

2 

4 

8 

16 

J?^        64 

12>8 

266            512! 

3 

9 

27 

81 

24»      721^ 

2187 

6561!        19683! 

4 

1& 

64 

256 

1024     409e 

16384 

(I'^ryM      262144i 

1  5 

25 

125 

625 

312i>,  li>62i> 

7-^125 

i    3t.K3ei25i     19531251 

6 

36i216 

1290 

7770'  4(')056 

279936 

'  1679616^  100776901 

7 

49'3i3;2401 

.UM)?  117649 

e2a543 

i  5764801 j  40353607! 

8 
9 

64512: 4Ci9(7 

o27G8  262144 121)97 15x1 

16777216:134217728! 

8i:729i,a50i 

59040  5i3144i!47S2f>i>94:]04072i;38742()489i 

EXAMPLES. 

1.  "VVTiat  Ls  the  sqiua-e  of  8?  Au's.  64. 

2.  What  in  the  square  of  9?  Ane.Sl. 
What  h  the  cul^e  of  4  ?  Ana.  64. 
What  h  the  cube  of  5  ?  Ans.  125, 
What  is  the  cube  or  thiiti  power  of  .263  ? 

Alls.  .018191447. 
What  is  the  Gth  pow^r  of  2.8  ?       Ans.  481.890304. 


What  i.s  the  8tk  power  of 


Aufs. 


zjT,  n  • 


The  root  of  a  uiunber  is  that  which  y,'ill  produce  that 
n amber  by  b*'.iug  multiplied  by  itself  a  giTen  number  of 
time-a ;  thus,  2  ie  the  gquore  root  of  4,  because  twice  2  make 
4  J  and  4  is  the  cub<>  rc^ot  of  64,  kx'ause  4  X  4  X  4= make 
64 ;  and  so  on. 


SQUAKE  BOOT. 

"N^lien  the  square  root  of  any  given  number  ia  required. 


RULE. 


Separate  the  given  number  into  periods  of  two  figures 

each,  begining  at  the  units*  place,  find  the  gi'eatest  square 

,|  contained  in  the  left  hand  period,  and  set  its  root  on  the  right 


«)R>aiisn«r*n««i«ai«M 


•  SQUARE   KOOT.  115 

of  tlic  given  number.  Subtract  said  square  from  the  left 
hand  period,  and  to  the  remainder  bnng  down  the  next 
period  for  a  dividend,  iid.  Double  the  root  for  u  divis-jr, 
and  tiy  how  often  this  divisor  is  contained  in  the  dividend, 
omitting  the  last  figure,  and  pkce  th(^  result  to  the  right  of 
the  asoertaiucd  root ;  and  to  the  right  of  the  number  pro- 
duced by  doubling  the  ascertained  root.  Multiply  and  sub- 
tract as  in  division ;  and  bring  down  the  next  period  to  the 
remainder  for  a  dividend.  Doul^le  tlie  ascertained  root  for 
a  divisor,  and  pi-oceed  as  before,  till  all  the  penoda  are 
bro\ight  down. 

JYoie.  If  the  square  root  of  a  whole  number  and  decimal 
.'iro  roquu*ed,  point  the  whole  number  from  right  to  left; 
then  l>egin  with  'the  decimal,  atid  point  from  left  to  right; 
if  there  be  only  one  figure  at  the  last,  place  a  cipher  to  ita 
right  to  make  an  even  period. 

EXAMPLKf. 

1.  What  in  the  sfjuare  root  of  451581  i* 

'45.15.8  l(Ans.  672  root. 
SG 


127)915 

sm 

1342)2684 
2684 

2.  What  is  the  square  root  of  106929  ?  •  Ans.  827. 

3.  AVhat  is  the  square  niot  of  6.9169  *r*  Ans.  2.63. 

4.  What  is  the  squai'c  root  of  393756  ?  Ans.  627.  -f 

5.  What  is  the  square  root  of  10.4976  ?  Ans.  8.24. 

6.  What  is  the  square  root  of  18.3021  ?  Ans.  4.28.  -j- 

7.  What  is  the  square  voot  of  1'60000  ?  Ans.  ioO. 

8.  W^hat  is  the  square  root  of  .250000  't  xiug.  .500. 

9.  "What  is  the  square  ryot  of  5  ?  Ans.  2.2S.  -f 

AVc.     When  the  squai*e  root  of  a  vulgar  fraction  is  re- 
quired, extract  the  squai'e  root  of  the  numerator  for  a  new 


jilt)  tJQUARE   ROOT.  '  ^ 

uunierator^  aud^  the  square  root  of  the  dcnoiniuator  fur  a 
new  Je nominator.  If  tliere  be  a  remainder,  cither  to  the! 
numerator  or  denominator,  reduce  the  fraction  to  a  decimal, 
and  extract  the  square  root  thereof;  or  if  there  be  a  mixed 
'  number,  reduce  it  to  an  improper  fraction,  and  proceed  as 
before, 

10.  Whut  is  the  square  root  of  \m?  Ana.  4. 

1 1.  What  is  the  square  root  of  flf ^ '/  Ans.  i- 

12.  AVhat  is  the  square  root  of  ^^^j  ?  Ans.  |. 

13.  What  is  the  square  root  of  f^g  ?  Anu.  f . 

14.  What  is  the  square  root  of  27A?  Ans.  5^ 

15.  What  is  the  square  root  of  30^  ?  Ans.  6/5. 

» 

16.  A  certain  yoHng  man  gave  484  apples  to  a  number 
of  gii-ls,  each  girl  received  as  many  apples  as  there  were 
L':irls  ;  how  many  girls  were  there  ?  An?.  22. 

17.  A  person  being  desirous  to  lay  off  3  acres,  2  roods, 
5  poles  of  land,  in  such  ^  manner  as  to  form  a  square  field, 
what  must  be  the  length  of  one  of  its  squares  ? 

Ans.  23.76  poles.  + 

18.  The  square  of  a  certain  number  is  124600,  what  is 
that  number  ?  Ans.  352.  + 

J^ote.    To  find  the  longest  side  of  a  right  angled  triangle. 
I  Squai-e  each  number,  and  extract  the  s([uare  root  of  their 
sum.     If  the  shortest  side  be  required,  extract  the  square 
root  of  their  difference. 

10.  Suppose  two  men  depai-t  fr^m  Baltimore;  one  of  them 
travels  due  east  90  miles;  the  other  duo  north  40  miles; 
how  far  are  they  asunder?  Ans.  98.48  miles.  + 

20.  Suppose  a  wall  be  20  feet  high,  and  be  suiTOunded 
by  a  creek  50  feet  wide ;  how  long  luu.s't  a  line  be  to  reach 
from  the  top  of  the  wall  to  the  opposite  bank  of  the  creek  ? 

Ans.  53.85  feet.  + 

21.  Said  James  to  Joseph,  I  see  a  tree  known  to  be  100 
feet  high,  ajjd  from  the  spot  where  T  stand  it  is  40  feet  to 
its  root,  but  I  demand  the  distance  from  where  I  stand  to 
its  top?  '  '*!>  •■'^'    '  Ans.  107.70  feet. 

22.  A  certain  castle  which  is  45  feet  high,  is  surrounded 


CUBE  HOOT.  117 

by  a  ditch  CO  feet  broad.  What  k>ngth  mu»t  a  ladder  be 
to  reach  from  the  outside  of  the  ditcli  to  the  top  of  the 
castle  ?  Ails.  75  feet. 

28.  What  is  the  height  of  a  st^.eple,  when  a  line  204  feet 
llciRg  -will  reach  from  the  top  of  the  steeple  to  the  opposite 
)>ank  of  a  river,  known  to  be  41  feet  broad  ? 

Ans.  199.83  feet.  +, 

24.  A  certain  general  has  an  army  of  5625  men;  how 
many  must  he  place  in  rank  and  file  to  form  them  into  a 
square  ?  Ans.  75  men. 

25.  Suppose  a  ladder,  60  feet  long,  be  so  planted  as  to 
reach  a  window  o7  feet  from  the  ground  on  one  side  of  the 
street,  and  without  moving  it  at  the  foot  %vill  reach  a  win-^ 
dow  23  foet  high  on  the  other  side.  What  is  tlie  breadth 
of  the  sti^eet?  Ans.  102.64  feci 


CUBE  ROOT 

When  the  cube  root  of  any  number  is  required. 

RUIiE. 

1st.  Separate  the  given  number  into  periods  of  three 
figures,  each  beginning  at  the  units'  place.  2nd.  Find  the 
greatest  cube  contained  in  the  left  hand  period,  and  set  its 
root  on  the  right  of  the  given  number,  ord.  Subtract  said 
cube  from  the  left  hand  period ;  bring  down  the  nest  period 
to  the  remainder  for  a  dividend.  4th.  Squai-e  the  root  and 
multiply  the  sc(uare  by  3  for  a  defective  divisor.  5th.  Try 
how  often  the  defective  divisor  is  contained  in  the  dividenrl, 
omitting  the  two  right  hand  figures,  and  place  the  number 
of  times  it  is  contained  to  th(!  right  of  the  ascertained  root, 
and  its  square  to  the  right  of  the  defective  di^'isor,  supply- i 
ing  the  place  of  tens  with  a  cipher,  if  the  square  be  less 
than  10.  6th.  Multiply  the  la.st  figure  of  the  root  by  all 
the  figures  in  it  previously  ascertaiued;  multiply  that  pro- 
duct by  30 ;  and  add  tlieir  products  to  the  divisor  to  com- 
plete it.  7th.  IMultiply  and  suTjtract,  as  In  Division.  8th. 
x\nd  to  the  remainder  bring  down  the  next  period  for  a  new 
dividend.  0th.  Find  a  divisor  as  before  :  and  thus  proceed 
until  all  the  pcriM.,-  are  brought  down.  '•* 


118 


SINGLE   POSITION. 


JVote.   "W^Iien  remaiuderrf  occur,  annex  ciphers  for  decimal 
periods;  and*f)oint  decimald  as  in  the  Squjire  Root. 


EXAMPLES. 

1.  What  is  the  cube  root  of  10793S61  ? 


Ans.  221 


10.793.861(221. 
8 

Defective  divisor  and  square  of  2  —  1204)2793 
+  120  =  complete  divisor  1324)2648 

Defective  diviRorand  square  of  1  =  145201)145.861 
-f  660  r~.  complete  divipor  145861)145.861 


2.  What  is  the  cube  root  of  16194277  ?  An8.  2 

3.  What  is  the  cube-root  of  5735339  ?  Ans.  1 

4.  What  is  the  cube  root  of  7532641  ?  Ans.  196. 

5.  What  is  the.cube  root  of  12.113847  ?  Ans.  ^:29. 

6.  What  is  the  cube  root  of  .378621  ?  Ans.  .72. 


I- 

53.  [ 
79. 

+  ! 
-f 


JS'otc.  When  the  cube  root  of  a  vulgar  fraction  is  required, 
reduce  it  to  its  lowest  terms,  and  extract  the  cube  root  of 
the  numerator  and  of  the  denominator.  If  there  be  a  re- 
mainder to  the  numerator  or  denominator,  reduce  the  frac- 
tion to  a  decimal,  and  extract  the  cube  root  thereof  When 
mixed  numbers  are  given,  reduce  them  to  improper  frac- 
tions, or  to  a  decimal,  and  proceed  as  before. 

7.  What  is  the  cube  root  of  f  f^^  ?  Ans.  -f. 

8.  What  is  the  cube  root  of  ^f^foV  ?  Ans.  ^^ 


9.  AVhat  is  the  cube  root  of  -|^  ? 


Ans.  3.32.  -f 


10.  There  has  been  a  cellar  dug,  out  of  which  has  been 
taken  3456  cubical  feet ;  what  is  the  length,  breadth,  and 
depth  of  it?  Ans.  15ft. -f- 


SINGLE  POSITION. 

Single  poBition  is  used  when  it  Ih  required  to  make  use 
of  only  one  .supposed  numI)or  to  find  an  unknown  number. 

RULE. 

Suppose  any  number  most  suitable,  and  proceed  with  it 


SINGLE   POSITION. 


119 


as  if  it  were  the  true  one ;  setting  down  the  result,  which  is 
the  firat  term;  the  given  number  the  second;  the  supposed 
number  the  third.  Proceed  by  Rule  of  Three.  The  quo- 
tient will  be  the  number  sought. 


EXAMPLES. 


1.  A  person  having  about  him  a  certain  number  of  dol- 
lars, said,  if  a  J,  a  J,  and  a  J,  were  added  together,  the  sum 
would  be  90 ;  how  many  hyd  he  ? 


12  (SuppoMed.) 
1 

2 


120 


40 
30 

20 


9   :  90  :  :  12  (Ans.  S120.     $90  proof. 

2.  A  merchant  received  a  number  of  dollars,  said  },  ^,  ^, 
and  I  of  the  number  is  90;  what  number  of  dollars  has 
he?  Ans.  75. 

3.  A.  nnd  B.  having  found  a  purse  of  money,  disputed 
who  should  have  it;  A.  said  that  4,  y\,,  and  -^^  of  it  amoimt- 
ed  to  35  dollars,  and  if  B.  could  tell  him  how  much  was  in 
it  he  should  have  the  whole,  otherwise  he  should  have 
nothing ;  how  much  did  the  purse  contain  ?         Ans.  $100. 

4.  A  person  after  spending  }  and  J  of  his  money,  had 
265  dollars  left,  how  much  had  he  at  first?         Ans.  $160. 

5.  A  certain  sum  of  money  is  to  !)e  divi<led  among  5  men, 
in  such  a  manner  Ibat  A.  shall  have  ],  B:  -J,  C.  yV,  D.  v/^,  I 
and  E.  the  remaimlcr,  which  is  40  dollars;  what  i:^    Ihe 
rumi"  ^         v\ns.  .<?100. 

6.  A  gentleman  being  asked  his  age,  replied :  if  the  years 
of  my  life  were  doubled,  and  f^  of  the  product  divided  by  3, 
the  reiiult  would  be  14 ;  what  was  his  age?      Ans.  35  years. 

7.  In  a  certain  web  of  cloth  there  is  4  blue,  ■}.  black,  and 
9  yards  white,  how  many  yards  are  there  in  the  web  ? 

•  Ans.  54  yards. 

8.  A.  Yoiitl)  wiio  was  desirous  to  know  the  age  of  a  fair 
Miss,  to  whom  lie  had  made  iiis  addresses,  was  replied  to 
in  the  following  manner  :  If  you  multiply  the  years  of  my 
life  by  .'>,  ^  of  the  product  will  be  three  times  the  square 
root  of  llv     What  wa3  her  age?  Ans.  14  years.] 


120  DOUBLE   rOSITION. 


DOUBLE  POSITION. 

Double  Position  teaches  to  find  the   trae   number  by 

making  u«e  of  two  supposed  numberf^. 

RULE. 

Suppose  two  numbers  most  suitable,  and  work  with  each 
according  to  the  nature  of  the  question,  observing  the  errors 
of  the  result.  Multiply  the  errors  of  each  operation  into 
the  contrary  supposed  number.  If  the  errors-  be  alike,  i.  e., 
both  too  much  or  both  too  little,  take  their  dijGference  for  a 
divisor,  and  the  difference  of  the  products  for  a  dividend ; 
but  if  the  errors  be  unlike,  that  is,  one  too  great,  and  the; 
other  too  small,  take  their  sum  for  a  divisor,  and  the  sum 
of  the  products  for  a  dividend.     Proof  as  in  Single 'Position. 

EXAMPLES. 

1.  A.  B.  and  C.  would  di\dde  $100  among  them,  so  as 
that  A.  may  have  5  more  than  B.,  and  B.  10  more  than  C. 
The  share  of  each  is  required. 

Suppose       A.  60  Again  suppose  A.  45 

B.  45  B.  40 

C.  35  C.  30 

130  115 

100  100 

30  error  too  much.     15  error  too  much 
2d  suppo£ed  No.  45  SOletEuppos'dNo 

150  750 

120 


error  30     1350 
error  1 5       750 

difference  15  15)600( 

600  Ans. 


0 


Proof  100. 


■<Ba^<m"^w^<— I II  naiB!»t>'»WBM 


. 


ALLIGATION.  X21 

2.  A  laborer  engaged  himself  for  60  days  upon  these 
conditions ;  that  for  every  day  he  worked  he  should  receive 
one  dollar;  and  that  for  every  day  he  was  idle  he  should 
forfeit  50  cents.     At  settlement,  he  received  $27  50  cents 
How  many  days  did  he  work,  and  how  many  was  ho  idle  ?  ' 

^    -R      I.,   1  .u  ^  ^°^-  Worked  85,  idle  15  days. 

d.  Bought  cloth  for  a  coat  at  $6  per  yard,  and  linen  to 

me  It  at  U  per  yard      The  number  of  yards  was  12,  and 

the  whole  cost  $42 ;  how  many  yards  were  there  of  each  ? 

/t    A  /•  1.     .       ,  .        ,  ^^•^-  ^  7^'^^^  each. 

for  them  all,  $320,-  being  paid  at  the  rate  of  $24  pgr  ox, 
$16  per  cow  and  $6  per  calf     There  were  as  many  oxen 
as  cows,  and  four  times  as  many  calves;  how  many  wereii 
there  of  eax^h  ?  Ans.  5  oxen,  5  co;s,  and  20  calves. 

D.  A  man,  when  driving  sheep  to  market,  was  asked 
where  he  was  going  with  his  score  of  sheep?  who  answered 
he  had  no  scoje;  but  if  he  had  as  many  more,  half  as 
many  more,  and  two  sheep  and  a  half,  he  would  have  a 
score.     How  many  had  he?  Ans.  7  sheep. 


ALLIGATION. 


Alligation  IS  a  rule  for  mixing  simples  of  different  qualities 
m  such  a  manner  that  the  composition  may  be  of  a  middle 
quality  When  the  quantity  and  rates  of  the  simples  are 
given  to  find  the  rate  of  mixture,  compounded  of  their 


RULE. 


Find  the  value  of  each  quantity,  according  to  their  re- 
spectiye  costs;  then  divide  their  whole  valu?  by  the  sum 
of  the  several  quantities. 

EXAMPLES. 

1.  If  4  pounds,  at  20  cents  per  pountJ,  6  pcmnds,  at  25 
cents,  and  8  pounds,  at  30  cents  per  pound,  b^  mixed  toge- 
tner,  wliat  will  a  nound  of  th^  mi-rfnt.^  h^  «,^«*u  »  ^ 


-^ — .J  w^v*  ^  I.UIXUUC5,  ai  ov  cents  per  pound,  be  mi 
tuer,  what  will  a  pound  of  the  mixture  be  worth  ? 

^  ■'-'■'i     li  iiiii'- II      II  ,    ,1 


AEITHMETICAL   PROGRESSION. 
Jh.        Ctt. 

4  at  20  =  80 
6  at  25  =  150 
8  ai  30  =:    240 

18  i8)470(AnB:  26  cente.  -f 

86 

110 

T08 


2.  If  a  pcraon  liave  4  lb.  of  tea,  at  90  cents  per  lb.,  8  lb. 
at  75  cents  per  lb.,  and  G  lb.  at  110  cents  per  lb.,  to  mix 

\  together,  what  will  a  pound  of  the  mixture  be  worth  ? 

Ans.  90  cents. 

3.  If  4oz.  of  silver,  worth  75  cents  per  ounce,  be  melted 
with  Soz.,  worth  60  cents  per  ounce,  what  will  loz.  of  the 
mixture  be  worth  ?  *  Ans.  65  cents. 

4.  A  ffij-mer  mingled  20  bushels  of  wheat,  at  50  cents  per 
bushel,  36  bushels  of  rye,  at  40  cents  per  bushel,  with  30 
bushels  of  corn,  at  20  cents  per  bushel,  what  is  the  worth  of 
one  bushel  of  the  mixture  ?  Ans.  35^  cents.  + 

5.  A  grocer  has  2cwt.  of  coffee,  at  $25  per  cwt.,  4cwt.  at 
,S20  50  cents  per  cwt.,  p^nd  7cwt.  at  ^18  62^  cents  per  cwt., 
■1  which  he  will  mix  together;  what  will  Icwt.  of  this  mixture 
I  be  worth?  >    Ans.  ^20  l#i  cent;?.. 


AiRITHMETieAL  PROGRESSIQ-N. 

Any  mnk  or  series  of  numl^ere  increasing  or  decrc-asmg, 
lid  by  a  c<.'mmon  diflcrence  in  Arithmetical  Progression^  as 

I,  2^,3,  4,  5,  6^  —  6,5,4,3,2,  1;— 1,  3,  5,  7,9,  11  j  — 

II,  9,  7,  5,  3,  1.  There' are  live  things  to  be  particularly  ^ 
attended  to  in  Arithmetical  Protri-es&ianj  the  first  and  last  <§ 
tennri;  thf>  uiimbfU"  ol'  It-rniH;  lh»'  roinip.nn  diffenMiov  ;uul 
th^•  5um  of  fill  thr  Lt.-nii  ■. 


The  lirat  teirm,, coramoii  difference,  and  number  fti\  termsjj 
beicg  giyec,  to  fhid  the  but  term  and  Bum  cf  all  t.he  t^rms-jj 


AlUTHMETICAL  PROQREtihilON.  12U 


EULE. 

Multiply  the  number  of  terms  less  one,  by  the  common 
difference ;  to  that  product  add  the  first  term ;  the  sum  is 
the  last  term.  Add  the  first  and  last  tenns  together,  and 
multiply  their  sum  by  the  number  of  termp,  and  half  the 
product  will  be  the  sum  of  all  the  terms. 

BXAMPLlBS. 

1 .  What  in  the  laat  term  and  sum  of  all  the  terms  of  an 
Arithmetical  Progression,  whose  first  term  is  2  j  the  com- 
mon difference  4,  and  number  of  terms  13  ? 

number  of  tenns  13 — 1 3=  12     2  -f  50 = 52  first  &  last  terms, 
common  difference  4  18  number  of  terms. 


48 

156 

first  term.  -|-  2 

52 

the  last  tt^rm.    60 

2)676 

Sum  of  all  the  terms.  ' 

838  Answer. 

2.  A  man  sold  40  yards  of  linen,  at  2  cents  for  the  first 
I  yard,  4  cents  for  the  second,  increasing  2  cents  every  yard ; 

what  did  they  amount  to  ?  Aup.  ^16  40cts, 

3.  Bought  15  yards  of  linen,  at  2  cents  for  the  first  yard, 
4  cents  for  the  second,  6  cents  for  the  third,  &c.,  increasing 
2  cents  every  yard ;  what  was  the  cost  of  the  last  yard,  and 
what  was  the  cost  of  the  whole  ? 

Ans.  The  last  yd.  cost  30cts,— the  whole  $2  40cts. 

4.  Twenty  persons  gave  charity  to  a  poor  woman,;  the 
I  fii'st  gave  6  cents,  the  second  8  cents,  and  so  on  in  arithmo- 
I  tieal  progression ;  how  much  did  the  last  person  give,  and 
j  what  sum  did  the  woman  receive  ? 

i  Ans.  The  last  person  gave  44  cts, — she  received  $5. 

5.  A  man  on  a  journey  travels  the  first  day  10  miles,  the 
second  14  miles,  increasing  4  miles  every  day ;  ho"v^  many 
miles  did  he  travel  the  tenth  day,  and  how  many  miles  did 
he  travel  in  all  ? 

Ana.  Teoth  day  46  miles, — in  all  280  miles. 


ARITHMETICAL   PROGRESSION. 

6.  Suppose  a  number  of  stones  were  laid  a  yard  distant 
from  each  other  for  the  space  of  a  mile,  and  the  first  a  yard 
from  a  basket ;  what  length  of  ground  will  that  man  travel 
over  who  gathers  them  up  singly,  returning  with  them  one 
by  one  to  the  basket  ?  Ans.  1761  miles. 

CASE  2. 

When  the  two  extremes  and  the  number  of  terms  are 
given  to  find  the  common  difference. 

RULE. 

Subtract  the  less  extreme  from  the  greater,  and  di^ade  the 
remainder  by  one  less  than  the  number  of  terms;  the  quo- 
tient will  be  the  common  difierence. 


EXAMPLES. 

7.  The  extremes  being  20  and  40 ;  and  the  number  of 
^  terms  6 ;  what  is  the  common  difierence  ? 


Ishimber  of  terms  6'  40  r  Extremes. 


1  20  }^^^.^ 

One  less  5        5)20 


Ans.  4  Common. 

8.  A  man  had  10  sons  whose  several  ages  difiered  alike ; 
the  youngest  was  3  years  old,  and  the  eldest  48 ;  what  was 
the  common  difference  of  their  ages  ?  Ans.  5  years. 

9.  A  man  is  to  travel  from  Boston  to  a  certain  place  in  9 
days,  and  to  go  but  5  miles  the  first  day,  increasing  every 
day  by  an  equal  excess,  so  that  the  last  day's  journey  may 
be  37  miles.     Required  the  daily  increase. 

Ans.  4  miles. 

10.  A  man  received  charity  from  10  different  persons- 
the  first  gave  him  4  cents,  the  last  49  cents,  in  arithmetical 
progression;  what  was  the  common  difierence,  and  what 
did  the  man  receive  ? 

Ana.  Received  $2  65cts. — common  difference  5cts. 


GEOiMLTRICAL   rROGKESSlON 

11.  When  a  debt  is  paid  at  8  different  pavments  in 
an  hmetol  progres^on,  the  first  payment  to  K^^the 
last  §l/o;  what  13  the  common  difference,  and  what  pa.h 
payment,  and  what  was  the  whole  debt  ? 

Am.  Common  difference,  ?22-Socond  payment  8-13- 
Third  payment,  §65,  &e.-The  whole  sum,  8784     ' 


GEOMETIUCAL  niOGRESSION. 

j     Oeonietrical  rrogre,ssion  is  the  increase  of  a  series  of 

«umber.s  by  a  common  nmltiplier,  or  decrea.sc  by  a  common. 

divisor,  as  4  8,  10,  'jo,  iU-U,  32,  l(i,  8,  4.     Thomul  I 

.pher  or  d.vsor  by  which  any 'series  is  iLroascd  or  de 

crcSgcd,  is  called  the  ratio. 

I  CASE. 

To  End  the  lawt  term  aud  sum  of  the  series. 

RULE. 

liaise  tlie  ratio  to  a  power  whose  index  is  one  less  than 
he  number  ot  terms  given  in  the  sum.  Multiply  the  pro 
duct  by  the  first  t<3rm,  and  that  product  by  the  ratio.  FrC 
this  last  product  subtract  the  first  term/and  divide  the  r^ 
mainder  by  a  number  that  is  one  less  than  the  ratio.  The 
quotient  will  be  the  sum  of  the  series. 


EXAMPLES. 


fi   !*  /^^  Y'^1 1^  ^"^^^^^^  ^^  ^^'^^^  and  pay  2  cents  for  the 


to  the  last^  how  much  must  I  pay  ? 


126  GEOMETRICAL  PEOGUEtSBION. 


o 

j     Eatio2,      -i,     8,    10,    ;>2,    6i,    128, 
'   .  128 

1024 
256 

128 


i^ 

tw 

tw 

Uh 

u 

Cj 

O) 

o; 

<y 

<a 

^ 

^ 

^ 

fc 

^ 

a 

a 

o 

a 

9 

T3 

•=!-( 

.c? 

rd 

►xa 

^ 

d 

ti 

♦  ' 

4J 

■*i 

?i 

CO 

-^f' 

ViTi 

ts> 

t- 

16884  14th  power, 
8  iird  power. 

131072  ITtli  pov.-Hr, 
2  Fir^t  term. 


2  Katio. 

524288 

2  Fii'st  torni. 

Divide  by  Katiu  2  —  1  =:  1)524286 

Au3.  15242  86  cte. 

2  A  man  taught  Bckool  21  days,  aad  received  for  the 
iirst  day  1  cent,  for  the  second  2,  for  the  third  4,  and  so  on, 
until  the  last.     What  sum  did  he  receive  ? 

Ans.  20,971  dollars  51  cents. 

3.  A  gentleman,  wliose  daughter  wiis  married  on  a  New 
Year's  day,  gave  her  81,  promising  to  triple  it  on  the  &st 
day  of  each  month  in  the  year.  What  did  her  portion 
amount  to  ?  Ans.  ^265,720. 

4.  What  sum  would  purchase  a  howe  with  4  shoes,  and 
six  nails  in  each  shoe,  at  ^  of  a  cent  for  the  first  nail,  a  half 
for  the  second,  a  cent  for  the  thii'd,  &c.,  doubling  to  the 
last?  Ans.  $41,943  03|  cts. 

5.  A  merchant  sold  20  bushels  of  clover  seed,  at  1  cent 
for  the  first  bushel,  4  for  the  second,  16  for  the  third,  and 


COMPOUND   INTEREST,    IJY    DECIMALS.  127 

SO  on ;  in  quadruple  proportion.  What  sum  did  be  receive, 
and  how  much  did  he  gain  by  the  talc,  supposing  he  gave 
!$5  per  bushel  for  the  seed  i'  ' 

.        (  ^3,GG5,038,750  25  cts,  sum  received. 
-^^^-  I  ?3,GG5,038,G59  25  eta.  gained. 


COMPOUNl)  IxNTEREST,  BY  DECIMALS. 

.  The  ratio  in  Compound  Interest  ia  the  amount  of  1  dollar 
for  1  year,  which  is  found  ;is  follows : 

100  :  104  :  :  1     (101  amount  for  1  year  at  4  per  cent. 

.Yote.  The  4<h  root  of  the  ratio  will  be  the  quarterly 
amount — the  s-^uarc  r(>ot  the  half  3(^arly  amount — and  the 
product  arising  from  the  half  yearly  and  quarter  yearly, 
multiplied  together,  the  three  quarter  yearly  amount,  as 

follows : 

Thus:    V  1.04  —  1.009853,  quarterly  amount;  and 
V  1.04=:  1.019804,  half  yearly  amount;  then  1.009853  X 
1.019804  =  1.029852,  amount  for  3qrs.  of  a  yeai-,  at  4  per 
cent.  « 

.Xotc.  The  4th  root  is  found  by  extracting  the  square 
root  of  the  square  root.  The  ratio  involved  to  the  power, 
whose  index  is  the  time,  ia  the  amount  of  one  dollar  for 
that  'time,  as  a  square  for  two  years,  a  cube  for  three 
yeai-s,  &c. 

Thus :  1.04  X  1.04  X  1.04  =  1.154864,  amount  of  1  del- 
lar  for  three  years,  at  4  per  cent. 

When  the  ratio  is  to  be  involved  to  years  and  quarters, 
the  power  for  the  years  must  be  multiplied  by  the  quarterly 
amount. 

Thus :  1.1910160  x  1.014674  ==.  1.2184929,  amount  for 
3  J-  yeai's,  at  6  per  cent. 


The  power  of  1  dollar  may  also  be  obtaino<l  for  months 
and  days,  nearly,  by  adding  the  monthly  simple  interest  of 


di 


128  COMPOUND   INTEREST,   BY   DECIMALS. 

1  dollar,  or  proper  pcirts  thereof,  to  the  amount  of  the 
quarter  next  preceding  the  given  time,  for  what  that  time 
exceeds  the  said  quarter,  as  follows : 

Amount  for  |  year,  =1.0295-63:  For  4|  years,  =1.318873 

Int.  of.nforlmo.,  =  .005000    .005000 

One  sixth  for  5  days,  =  .000833     .000833 


For7month9,5days=1.035396.for4y.l0mo.5d.=1.324706 


TA.BLE  I. 

9moimt  of  $1  for  a  year,  and  for  Quarters j  at  Compound 

Interest. 


Rate 

For  three      For  two 

For  one 

Simple  Int. 

pr.  ct. 

3 

Ratio. 

Quarters. 

Quarters. 

Quarter. 

of  $1  for 
1  month. 

1.03 

1.022416 

1.014889 

1.007417 

.002500 

3^ 

1.035 

1.026137 

1.017349 

1.008637 

.002917 

4 

1.04 

1.029852 

1.019804 

1.009853 

.003333 

4^ 

1.045 

1.033563 

1.022252 

1.011065 

.003750 

5 

1.05 

1.037270 

1.024695 

1.012272 

.004167 

5i 

1.055 

1,04097^ 

1.027132 

1.013475 

.004583 

6 

1,06 

1.044671 

1.029536 

1.014674 

.005000 

6* 

1.065 

1.048364 

1.031988 

1.015868 

.005417 

7 

1.07 

1,052053 

1.034408 

1.017058 

.005833 

COMPOUND   INTEREST,   BY    DECIMALS. 


1:^9 


TABLE  2,    Showing  the  amount  of  one  dollar  from  one  year  to  fortj"? 

5^  per  cent 


1 

2 


8 

9 

10 
11 
12 

il31 
141 


4  per  cent. 


15 
1 10 

;i7 

1 18 
19 
20 
21 
122 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 


4 
4 
404 


.0400000 
.0816000 
.1248640 
.1698585 
.2166529 
.2653190 
.3159317 
.3685690 
.4233118 
.4802442 
.5394540 
.6010322 
.6650735 
,7316764 
,80(/l)43r-) 
.8729812 
,9479005 
,0258161 
1068491 
1911231 
2787680 
3699187 
4647155 
5633041 
6658363 
7724697 
8833685 
.9987033 
.1186514 
.2433975 
.3734324 
.5080587 
.6481831 
.7943163 
.9460889 
4.1030325 
4.2680898 
,4388134 
,6163659 
,8010206 


4i  per  cent. 

ToTsoooo 

.0920250 

.141166111 

.19251861 


5  per  cent. 

"^0500001)  1 

.1025000  1 

1576250!l 


.2461819 
3022601 
.3608618 
4221006 
.4860951 
1.5529694 


.6228530 

.6958814 

.772J961 

.8519449 

.9352824 

.0223701 

.1133768 

.2084787 

.3078603 

.4117140 

,5202411 

,6336520 

,7521663 

,8760138  3. 

,0054344 

,14(16790 

,2820095 

,4296999 

,5840364 

7453181 

9138574 

,0899810 

,2740301 

4663015 

6673478 

8773784 

0968604 

3262192 

5658990 

8163645 


.2155062 

.2762815 

.3400956 

.4071004 

.4774554 

.5513282 

.6238946 

.7103393 

.7958563 

.8S56491 

.9799316 

.0789281 

.1828745 

.2920183 

.4066192 

.5269502 

.6532977 

.7859625 

.9252607 

,0715237 

2256999 

3863549 

5556726 

7334563 

9201291 

1161356 

3219423 

5380394 

7649414 

0031885 

2533473 

5160152 

7918101 

0314009 

3854772 

7047511 

0399887 


.0550000 

.1130250 

.1742413 

.2388246 

.3069698 

.3788426 

.4546789 

.5346862 

.6190939 

.7081440 

,8020919 

,9012069 

,0057732 

,1160907 

,2324756 

,3552617 

4848011 

6214652 

7656458 

,9177563 

0782329 

2475357 

4261502 

6045885 

8133919 

0231279 

2443999 

,4778419 

7241232 

9839469 

2580671 

5472608 

8523600 

1742398 

5138230 

8720832 

2500478 

6488004 

0694844 

5133060 


6  per  cent. 


1.0600000 

1.1360000 

1.1910160 

1.2624769 

1.3S82256 

1.4185191 

1.5036302 

1.5938480 

1.6894789 

1.7908476 

1.8982985 

2.0121964 

2.1329282 

2.2609039 

2.3965581 

2.5403517 

2.6927727 

2.8543391 

3.0255995 

3.2071355 

3.3995636 

3.6035374 

3.8097496 

4.0489346 

4.2918707^ 

4.5493829 

4.8223459 

5.1116867 

5.4183870 

5.7434912 

6.0881007 

6.4533867 

6.8405899 

7.2510253 

7.6860868 

8.1472520 

8.6360871 

9.1542523 

9.7035074 

10.2857178 


180  COMPOUND   INTEREST,   BY   I)E0Ii\fAL8. 

Oompound  Interest  in  that  in  wliicli  the  interest  of  1  year 
is  added  to  the  principal,  and  that  amount  is  the  principal 
for  the  second  year,  and.  so  on  for  any  number  of  years. 


CASE  1. 
The  principal,  time  and  rate  given  to  find  the  amount. 

RULE. 

Multiply  the  principal  by  the  ratio  involved  to  the  time, 
which  may  be  taken  from  table  2,  and  the  product  will  be 
the  amount,  from  which  subtract  the  principal  for  the  com- 
pound interest, 

EXAMPLES. 

1.  What  13  the  compound  interest  and  amount  of  1300 
for  3  years,  at  5  per  cent.  ? 

1.05  X  1.05  X  1.05=1.1576250 

800 


r  $347.28.7.5000  amount! 
Answer.  )    300 

(    S47.28. 7  interest. 

2.  What  is  the  amount  of  $500  for  five  years,  at  G  per 
cent.?  Ans.  S669.11.2. 

3.  What  is  th«  compound  interest  of  ^100  for  four  years, 
at  5  per  cent.  ?  Ans.  $21.55. 

I     4,  What  is  the  amount  of  five  dollars  for  20  years,  at 
«ix  per  cent.  ?  Ans.  $16.03.5. 

5.  What  is  the  compound  interest  of  1000  dollars  for 
thirteen  years,  at  six  per  cent,  per  annum  ? 

Ans.  $1132.92.8. 

6.  What  is  the  amount  of  50  dollars  for  11  yeai*s,  at  6 
J  per  cent.  ?  Ans.  $94.91.4m.  -f 

7.  What  ia  the  amount  of  12  dollars  for  one  half  year, 
I  at  6  per  cent.  ?  Ans.  812.85.4. 


I'EKMUTATION. — COMBINATluN,  131 1 

CASE   2.  _  I 

The  amount,  time,  and  rate  per  cent,  giveu  to  find  the  I 
principal.  } 

RULE. 

Divide  the  amount  Ly  the  ratio  involved  to  the  time  in  j 
table  2. 

EXAMPLES. 

1 .  What  principal,  put  to  interest,  will  amount  to  $400 
in  five  year^j  at  6  per  cent.  ? 

1.3382256)400:0000000         Ans.  $298.90.3. 

2.  What  principal,  put  to  interest,  will  amount  to  ^1500 
in  7  years,  at  5^  per^cent.  ?  Ans.  81031.15*.  -f 


PERMUTATION. 

Permutation  iri.uscd  to  show  how  many  waya  things  may 
be  varied  in  place  or  succesBion. 

RULE. 

■  Multiply  all  the  terms  of  the  series  continually,  from  one 
to  the  given  number,  inclusive,  and  the  last  product  will  be 
the  answer  required. 

EXAMPLES. 

■     1.  In  how  many  diflferent  poyitions  can  ten  persons  place 
themselves  round  a  table  ? 

Ix2xs!v4'>c5x6x7x8x9x  lO^Ans.  3628800 

2.  The  church  in  Boston  has  8  bells;  how  many  changes 
may  be  rung  on  them  ?  'Ans.  40320. 

3.  In  what  time  will  a  person  make  all  the  changes  that! 
I  the  fir.st  12  letters  of  the  alphabet  admit  of,  allovring  151 
i  seconds  to  eaeli  change,  and  365  J  days  to  a  year. 

I  _      Ans.  227y.  248da.  6h. 

COMBINATION.   ' 

Combination  is  used  lo  filiow  how  many  different  wayj' 
a  less  nuiubor  of  lhinn;3  can  be  combined  oul  uf  a  greater, 
I  as  out  of  the  figures  1,  2,  3,  4;  four  combinations,  12,  21, 
I'oi  and  43,  may  bo  VLilbrmKl 


132  DUODECIMALS 


RULE. 

Take  a  series  proceeding  from  and  increasing  by  a  unit 
up  to  the  number  to  be  combined.  Take  another  series  of 
as  many  places  decreasing  by  unity  from  the  number  out  of 
which  the  combinations  are  to  be  made.  Multiply  the  first 
continually  for  a  divisor,  and  the  last  for  a  dividend,  the 
(j^otient  will  be  the  auswsr. 

EXAMPLES. 

1.  How  many  combinations  of  4  persons  in  8  ? 

1x2x3x4=     24  24)1680(70  Ans. 

8x7x6x5  =  1680  168 


0 

2.  How  many  combinations  of  10  figures  may  be  made 
out  of  20?  .    Ans.  184756. 

3.  How  many  changes  may  be  rung  with  10  bells  out  of 
20?  Ans.  184756. 


DUODECIMALS. 

Duodecimals  are  parts  of  a  foot;  the  denominations  of 
which  increase  continually  by  12.     The  denominations  are, 

♦  12  fourths  ("")  make  ...  1  third.'" 

12  thirds         1  second." 

12  seconds 1  inch.  in. 

12  inches        i  foot,  ft 


AD'DITION  OF  DUODECIMALS. 


RUL'E. 


Proceed  as  in  Compound  Addition,  observing  to  cairy 
one  for  every  12.  - 


DUODECIMALS.  13^ 

EXAINIPLES. 

,^^   ft    *?'     ft'    in.     ' 

8    10      9    11  i!2      8      7      1    '4 

13      7    10      8  15    11      9      8    10 

1^    1^      5 2  13      0      0      1 

Ans.  49      2      3      5        Ans.  150    "e      6~"^      9 
3.  Three  planks  measure  as  follows:  16ft.  Sin  —14ft 
6in.— 17ft.  9m.  2".     How  many  fe<  .t  do  they  conta In  ? 

Ans.  48ft.  llin.  2". 

SUBTRACTION  OF  DUODECIMALS. 

RULE. 

Proceed  as  in  Compound  Subtraction,  observing  the  12's. 

EXAMPLES. 

Jt.    lit.  fl         l^      II      III      ,,n 

17    5    10  11    4  887    9    6     14 

Ans.  32    9      0    9    9  A:is.  12  11    1    9    8 

41ft..  7m.,  how  much  wiU  be  left?  Ans.  21ft.  9in, 


MULTIPLICATION  OF  DUODECIMALS. 

RULE. 

Set  the  multipHer  in  such  a  manr  er  that  the  feet  thereof 
may  stand  under  the  lowest  denom nation  of  the  riultipli- 
cand;  multiply  and  carry  one  for  jyery  12  from  one  de- 
nomination to  another;  and  taie  parts  for  the  inchts,  as  lu 

JVofe.    Feet  multiplied  by  feet,  gi 76  feet 

Feet  multiplied  ^  inches,  give  inchei. 
Feet  multiplied  by  seconds,  give  seconds. 
Inches  multiplied  by  inchc  s,  give  seconds. 
Liches  multiplied  by  eeoor  ds,  give  thirds. 
Seconds  multiplied  by  seconds,  give  fourths 
^f=  "      


i.>4  niOMISCUOTJS   EXAMPLES. 

EXAMPLES. 

L  Multiply  5ft.  6m,  by  2ft,  4m. 

ifu         ft.     in. 
4  I  si  f  5       6    • 


=^ 


o. 


11       0 

1     10 

-     Alls.    iSft.'iOiii. 

J.Iultiply  54ft.  lOin.  by  5ft.  7m.     Aus.  SOGft.  liu.  10'. 
jMultiply  Oft  Till,  by  oft.  Gin.         Aiis.  33ft.  Gin.  G". 

4.  V/hat  are  the  contents  of  a  dooi';  measm'iug  in  length 
6ft.  Oin.  3",  and  in  width  3ft.  Sin.  ? 

- .     Aps.  23ft.  lin.  7"  3'". 

5.  A  certain  partition  is  81ft.  lOin.  4"  long,  and  14ft. 
Tin.  5"  hi<'b.     How  many  yards  does  it  contain  ^ 

Ans.  132yd.  8ft.  Tin.  9"  T"  8"". 

G.  If  a  lloor  be  T9ft.  4in.  by  38ft.  llin.,  bow  many 
square  feet  arc  there  in  it?  Ans.  3100ft.  4in.  4". 

T.  How  many  square  feet  in  a  board  ITft.  Tin.  long,  and 
Iff.  5iu.  wide?  Aus.  24ft.  lOin.  11". 

8.  AVhat  will  be  the  expense  of  pla^t^riug  the  walls  of  a 
room  8ft,  Gin.  high,  and  each  of  the  four  gidee  IGft.  oip. 
lonp;,  at  50  cents  per  square  yard  ?    '  ;        Ans.  ^30  69.  4- 

9.  In  40  planks,  13ft.  long  and  8iu.  wide,  how  many 
feet?  tAif  :'.'H<I<.)'  •  Ans.  34Gtft. 
1  10,  lu  49  plauk.s,  22ft.  long  and  llin.  wide,  how  many 
I  feet?                                      ^    '                  Ans.  988ft.  2in. 

11.  In  17  plankn,  12ft.  long  and  5in.  wide,  how  mrmy 
^■fect?  '>A^s.  85  feet.-[{i 


:  PROMISCUOUS  EXAMPLES. 

1.  How  many  bushels  of  cora^  at  22  cents  per  bushel, 
can  I  have  for  40  dollars-?  ,,r.x»^  ri        ^        A.ns.  181y\l)u. 

2.  If  a  B?4a's  yearly  inq9pie^"bo  $7777,  how  much  is  it 
:per  day?  ,  ••  ,,;  '  \  v,:,.  •  Ana.  $21  SQeta.  6m.  + 
..    C.  My  ^eut  sends  mu  woid  ho  hai;  bought  goods  to  the 


4*:^ 


11  TROMiscuous  examples;.  llj5 

value  of  500  dollars  54ct.s.  upon  my  ax^count;   what  will 
I  ins  commission  come  to  at  4  per  cent.  ? 

A    A  1   J.    ..    Y    ,   .  Ans.  20  dollars  2cts.+ 

4.  A  man  had  m  his  desk  2176  dollars  55  cents,  he  drew 

out  at  one  tmie  13  dollaxs  6^  cents,  at  another  time  49 lol^ 

ars  1  cent,  and  at  another  61  dollar's  21 1  cts.,  after  which 

, he  deposited  at  one  time  88  dollars  884  cts.:  how  much 

I  had  he  in  desk  after  making  the  deposit  ?  ' 

I     r^    A    •   Of:  ,.   T.  .  Ans.  $2142  14i  cents. 

5    A.  IS  25  years  old  B.  15  years  older  than  A.,  and  C 

1}LT'"  '^^"'  '^""  ^-     ^^^  '-^Ses  of  R  and  C.  are  re- 
^ TVm«v.i       .    ,    .  Ans.B.40y.  a52y.' 

6.  Sold  6  bnles  of  doth,  5  of  which  contained  10  pieces 
eacOi  and  m  each  piece  were  28  yards;  the  other  bale  con- 
tamed  16  pieces,  and  m  ejich  piece  were  20  yards.  How 
many  pieces  and  how  many  yards  wore  there  in  aJl  ? 

7    T^       J      , .  t.  . ,  ^^"^'  ^^  V^^^^s,  and  1720  yds. 

7.  If  goods  which  cost  44  doUajs,  be  sold  for  62  dollars 
what  IS  the  gam  per  cent.  ?  Ans.  40|^  per  cent! 

«.  If  4  of  an  ounce  cost  |  of  a  dollar,  what  will  %  of  a 

^TjTI,        11      ^      .  Ans.  ^19  (fo  cts. 

y.  It  I  of  a  gallon  cost  1^  dollars,  what  will  -«   of  a  ton 

I  """"Tn    I  s.  .  ^"^-  ^^10  90  c^s.  9m.  + 

,  W.  Al^erson  who  was  possessed  of  f  of  a  store,  sold  ^ 
of  his  share  for  551  dollars  62}  cents,  Uat  was  the  whole 
store  worth  at  that  rate  ?  Ans.  1241  dollars  15^  cents. 

u     Wliat  will  27cwt.  of  iron  come  to  at  U  56  cts  per 

lo    T^  V  1.      -.n.  Ans.  3123  12  cts. 

12.  If  I  buy  100  yards  of  cloth,  at  50  cents  per  yard,  at 
how  much  must  I  sell  it  per  yard  to  gain  100  per  cent.  ? 

iQ    "o      i-i  .       „  Ans.  $1. 

id.  Bought  a  quantity  of  soods  for  ^400,  and  5  months 
afterwards  sold  them  for  $650.  How  much  per  cent  per 
annum  was  gained  by  the  transaction  ?  ^     ,  "^-  P^r 

1/1    wTi.  A-'^T-    .  .  Ans.  150  per  cent. 

14.  What  IS  the  interest  of  ??51  62^  cents  for  2  years 
3  months,  and  13  days,  at  7^  per  cent  ?  ^       ' 

i     I'.    TTnwnff  ij  ,    Ans.  S8  85  cents. -f 

fn.  L  t7  ^^^^"^ould  a  wagon-Wheel  turn  round  in  roll- 
bo^fiOO  n  .f  "^^^J"^./,^  Baltimore;,  suppose  the  distance  to 

,  be.  600  miles;  admitting  the  wheel  be  5  feet  in  diameter  ? 

Ans.  201600  times. 


iOU 


136  PROMISCUOUS   EXAMPLES. 

16.  A  person  has  two  yilver  cups  of  unequal  weight, 
having  one  cover  for  both  which  weighs  5oz.,  now  if  the 
cover  b<^  put  on  the  less  cup  it  will  he  double  the  weight 
of  rhe  I  reater  cup,  and  put  on  the  gi'eater  cup  it  will  be 
throe  times  as  heavy  as  the  less  eup,  what  is  the  weight  of 
each  cup?  -Ans.  The  less  8  oz.,  the  greater  4  oz. 

17.  A  man  had  $20,  which  he  wished  to  lay  out  as  fol- 
lows :  viz.,  in  sugar  at  10  cents,  coffee  at  14  cents,  and  rice 
at  11  cents  per  pound;  so  as  to  have  an  equal  quantity  of 
each.     How  many  pounds  must  he  have  ?        Ans.  57^  lb. 

18.  A  Gom-erib  is  5f  c.  wide  at  the  bottom,  and  7ft.  wide 
at  the  top,  tell  me  how  wide  it  is  on  an  average  ? 

Ans.  6  feet. 

19.  When  .^25  are  n;ultiplied  by  125,  how  much  money 
is  there  in  the  product?  'Ans.  $625. 

20.  "When  $25  are  multiplied  by  25  cents,  how  much 
money  is  there  in  the  p  :'oduct  ?  Ans.  $6  25  cts. 

21.  When  25  cents  are  multiplied  by  25  cents,  how  much 
money  is  there  in  the  p:oduct?  Ans.  6  J  cents. 

22.  How  much  will  18|  bushels  of  corn  come  to  at  ISf 
cents  per  bushel  ?  *  Ans.  $3  51  cts.  5m'.  -1- 

23.  "What  will  2^  pounds  of  beef  come  to  at  2  J  cents 
per  pound?  Ans.  6j'cents. 

24.  In  48  planks  8  inches  wide  and  10  feet  long,  how 
many  feet?  Ans.  320  feet. 

25.  A  house  is  20  feet  long,  and  18  feet  wide.  How 
many  feet  of  plank  will  be  required  to  cover  the  floor  ? 

Ans.  360  feet. 

26.  What  is  the  neut  of  a  hog  weighing  294  pounds 
gross  ?  .  Ans.  256|  lb.  neat. 

27.  If  A.  can  drink  ;i  pint  of  whiskey  in  20  minutes;  B. 
oje  in  80;  and  C.  one  ;n  40;  in  what  time  can  they  drink 
a  pint,  when  all  drinking  together  ? 

rivideby20,  30,and40.  Suppose  120 

3 

•       4 

6 

13)120(Ans.  9A  min. 
117 


rdk    ^ 


PROMISCUOUS   EXAMPLES.  IXi] 

J\ytc.    Jn  imy  question  like  the  above,  suppose  an}^  num- 
ber into  which  all  the  given  numb ts  may  be  diviied  with 
out  any  reniRindcr,  then  add  together  theu'  quotients,  b) 
which  sum  divide  the  same  dividend.     The  quotient  will  be 
the  answer. 

28.  Three  young  ladies  mot  at  their  neighbours'  for  the 
pm-pose  of  tinishing  a  fine  quilt.  J^  aid  M.,  I  can  fi jish  it  in 
six  hours;  said  E.,  I  can  do  it  in  four  hours;  said  L.,  I  can 
do  it  in  three  hourn;  })ut  wo  will  all  work  t-ogether.  In 
what  time  can  we  finish  the  quilt  ?  Ans.  1 1  hours. 

29.  There  \s  a  cellar  dug,  that  is  20  feet  every  way  in 
length,  breadth  and  depth.  How  many  solid  feet  of  earth 
were  taken  out  of  it  ?  An?.  8000  feet. 

30.  How  many  bricks,  9  inches  long  and  4  inches  wide, 
will  pave  a  yard  that  is  300  feet  long  and  40  feet  ^vide"? 

Ans.  480C0  bricks. 
•81.  What  sum  will   produce  sa   much  interest   in   five 
years,  as  §^500  would  in  8  years  an  \  4  months  ? 

Anr.  8833  J. 
32.  A  guardian  paid  his  ward  ;?3500  for  I25C0,  which 
he  hnd  held  in  possession  8  years.     What  rate  of  interest 
did  he  allow  him  ?  Ans.  5. 

83.  A.  owes  B.  100  dollars,  payr.ble  in  o\  montlis;  8150 
in  4|  months,  auvl  $204  in  5f  months;  but  is  williiig  to 
make  one  p.nyment  of  the  whole.  In  what  time  should  the 
payment  be  made  ?  Ans.  4mo.  23  day.i.  + 

34.  In  what  time  will  any  sum  of  money  double  itself,  at 
5  per  cent,  simple  interest?  Ans.  20  years. 

35.  If  E.  can  do  a  piece  a  vfork  alone  in  10  dayj,  and  0. 
can  do  it  in  19  days,  iti  what  time  can  they  finish  it,  both 
working  together  i*        •  Ans.  r>||  days. 

36.  A.  E.  ani  0.  found  a  pui^^  of  money,  containing 
?60;  where^)f  A.  is  to  h&^i  f,  B.  i,  and  0.  i.  What  will 
be  the  sliare  of  each '/ 

C  A.'s  share  ^27  69  cents  2m.  + 

Ans.  i  B.'s  sLare  $18  46  cents  Im.  4- 

(C.'s  sh-ire  ^^13  84  cenfs  6m.  + 

87.  A.  and  B.  traded  to^etii-??;  A.  put  in  320  dollars  for 
five  months ;  B.  pnfc  m  480  dollar?  for  3  months;  and  they 

U*  --- ^ i 


138  I'llOMISCL'OUS   EXAMPLES. 

gained  100  dollars.     What  was  cacli  man's  share  of  the 
ggiu?  .     ,   (  A.'a  share  ^53  69cts.  Im.  + 

^^^'  I  B.'b  share  $46  30cts.  8m.  + 
80.  What  is  the  difTeroncc  between  tlie  interest  of  ^1000, 
at  6  per  cent,  for  8  years^  and  the  discount  of  the  same  sum 
for  the  same  timO;  and  at  the  same  rate  of  interest? 

Ans.  The  int.  exceeds  the  discount  by  ^155  GTcts.  5m. 

39.  Said  I)ick  to  Harry,  I  ca*  place  four  nines  in  such 
a  manner  that  they  will  make  precisely  an  even  hundrgd. 
Can  you  do  so  too  ?  Ans.  99||-. 

40.  What  is  the  sum  of  third  and  half  the  third  of  6} 
cents?  Ans.  3^  cents. 

41.  How  many  dollars  are  there  in  £200,  Tennessee  cur- 
rency? Ans.  $6(56  61|  cents. 

42.  The  clocks  -of  Italy  go  on  to  24  hours.  How  many 
strokes  do  they  strike  in  one  complete  revolution  of  the 
index?  '"'  Ans.  300. 

43.  A  line  40  yards  long  will  exactly  reach  from  the  tojD 
of  a  fort,  startling  on  the  ])vink  of  a  river,  to  the  opposite 
bank,  known  to  be  25  yards  from  the  foot  of  the  wall. 
What  is  the  height  of  the  wall  ?  Ans.  31.22yds. 

44.  What  is  the  value  of  a  slab  of  marble,  the  length  of 
which  is  5ft.  Tin.  and  the  breadth  1ft.  lOin.,  at  ^2  per  foot? 

Ans.  §20  47cts.  + 

45.  Shipped  to  New  Orleans  40001b.  of  cotton,  at  7^  cts. 
per  lb.,  and  513  yards  of  muslin,  at  62^  cts  per  j^ard;  in 
return  for  wJiich,  I  have  received  87cwt.  3qr.  of  sugar,  at 
12^  ceftts  per  pound,  and  44  pounds  of  indigo,  at  20  cents 
per  pound.     What  remains  due  to  me  ? 

Ans.  ^83  33 1  cents. 

46.  If  the  flash  of  a  gun  was  observed  just  1  minute  and 
20  seconds  before  the  report :  What  was  the  distance,  sup- 
posing the  flash  to  ])e  seen  the  inst^it  of  its  going  off,  and 
admitting  the  sound  to  fly  at  the  rate  of  1150  feet  in  a 
second  ?  Ans.  17m.  3fur.  15p.  4yd.  Oft.  6in. 

47.  There  is  a  certain  pole,  ^  of  which  is  in  the  water, 
I  in  the  mud,  and  6ft.  on  dry  groimd.  What  is  the  whole 
length  of  the  pole  ?  .^  Ans.  30ft. 

48.  When  J^  of  the  number  of  an  Assembly,  and  15, 
were  met,  there  were  J  and  10  absent.  How  many  did 
that  branch  of  the  legislature  consist  of?  Ans.  150. 


ril03IISCU0US    EXAMPLES.  139 

40.  Bonglit  goods  for  ^500,  and  sold  the  same  imiuo- 
liatcly  for  §400.     What  was  the  loss  per  cent.  ? 

Ans.  20  per  cent. 
60.  Wliat  is  the  interest  of  $15,000,000  for  one  niiuute, 
at  6  per  cent,  per  annum?  Ans.  ^1  71  cts.  2ra.4- 

51.  If  the  earth  be  360  degrees  in  circumference,  and 
each  degree  60  miles,  how  long  would  a  man  bo  in  travel- 
ling round  it,  who  advances  40  miles  a  day,  reckoning  365^ 
days  a  year?  Ans.  Iv.  174da.  18hr. 

"52.  Sold  12  yards  of  cloth  for  SI  5  20cts!',  by  which  was 
gained  8  per  cent.     What  was  the  first  cost  of  a  yard  ? 

Ans.  $1  17cts.  2m.  4- 

53.  Ijought  12  pieces  of  white  cloth  for  $16  50cts.  per 
piece;  paid  32  S7cts.  per  piece  for  dyhig.  For  how  much 
must  I  sell  them  each,  to  gain  20  per  cent.  ? 

Ans.  $23  24cts.  4m. 

54.  When  T,  by  disposing  of  a  yard  of  cloth  at  §7,  gain 
56 1  cents,  what  would  I  gain  by  selling  3  pieces,  which 
cost  me  8400  'i  Ans.  32  14:lcts.  + 

55.  The  yearly  interest  of  Charlotte's  money  at  6  per 
cent,  per  annum  exceeds  one  twentieth  part  of  the  principal 
by  $100,  and  she  does  not  intend  to  marry  any  man  who  is 
not  scholar  enough  to  tell  her  fortune.     I'ray  what  is  it  ? 

Ans.^  ^10,000. 

56.  There  is  a  cistern  having  eight  pipes  to  discliarge  it. 
By  the  first  it  may  be  emptied  in  ten  minutes ;  by  the  second 
in  20 ;  by  the  third  in  40 ;  by  the  4th  in  80 ;  by  the  5th 
in  160;  by  the  6th  in  320;  by  the  7th  in  640;  and  by  the 
8th  in  1280.  In  what  time  will  all  eight  running  together 
empty  it  'I  Ans.  5^^^  minutes. 

57.  In  140  planks,  each  12  feet  long  and  9  inches  wide, 
how  many  feet?  Ans.  1260. 

58.  At  a  certain  quilting,  I  of  the  girls  are  eating,  I  of 
them  cooking,  and  5  at  work;  I  would  know  how  many 
girls  there  arc  at  the  place  ?  •     Ans.  30. 

59.  A  hare  starts  12  rods  before  a  hound,  but  is  not  per- 
I  ccived  by  him  till  she  has  been  up  45  seconds,    .^he  scuds 

away  at  the  rate  of  10  miles  an  hour,  and  the  dog  on-s'iew, 
n'akes  after  at  the  rate  of  16  miles  an  hour,  llow  long 
will  the  course  hold;  and  wliat  space  will  be  run  over  from 
the  spot  whence  the  dog  started,  until  the  hare  be  over- 
taken ?        *  Ans.  228Sft.  and  97  J  sec. 


140  PROMISCUOUS   EXAMPLES. 

60.  Bought  a  -^^atch  at  10  per  cent,  under  its  value,  and 
sold  it  at  10  per  cent,  over  its  value,  and  by  so  doing  gained 
$10.     How  much  was  the  watch  worth  ?  Ans.  $50. 

61.  Bought  a  horse  and  saddle  for  $100.  The  horse  was 
worth  seven  times  as  much  as  the  saddle.  How  much  was 
the  horse  worth,  and  how  much  was  the  saddle  worth  ? 

.        (  H.  $87  50. 
^^^'  \  S.  $12  50. 

62.  A.  owes  B.  100  bushels  of  com,  the  tub  out  of  which 
they  expect  to  measure  the  same,  contains  Ibu.  Ipe^  Iqt. 
Ipt.     How  often  must  it  be  filled  to  make  the  100  bushels  ? 

Ans.  77/-^. 

63.  A  merchant  purchased  200  yards  of  broad  cloth,  at 
$3  per  yard.  A  customer  who  was  desirous  of  speculating, 
projwsed  to  take  $300  worth  of  the  cloth,  at  $2  75  per 
yard,  and  then  give  $3  25  for  the  remainder.  What  would 
the  merchant  gaiu  or  lose  by  the  transaction  ? 

^  Ans.  He  would  lose  $4  54  ,\. 


APPENDIX. 


MENSURATION  OF  SURFACES. 

To  find  the  area  of  a  ParalleJogram,  Square,  Rhombus 
or  Rhomhoid. 

3Iultiply   the   length    by    the   perpendicular   height   or 
breadth. 

EXAMrLES. 

1.  How  many  square  feet  arc  there  in  a  floor  23  J  feet 
long  and  18  feet  broad  ?  Ans.  23  J  X  18  =  423. 

2.  What  are  the  contents  of  a  piece  of  ground  66  poles 
square?  Ans.  4356po.  or  27a.  36po. 

3.  What  are  the  contents  of  a  rhombus, 
whose  sides  are  60  feet,  and  perpendicular 
50  feet? 

Ans.  3000  feet. 


4.  How  many  acres  are  there  ^^ 
in  a  field  in  the  form  of  a  rhom- 
boid, the  sides  of  which  are  50 
poles,  and  perj)endicular  distance 
25  poles  ?         Ans.  7a.  3r.  lOp. 

5.  How  many  square  feet  are  there  in  a  plank  13  feet 
long  and  7in.  broad?  Ans.  7ft.  84in. 

6.  How  many  square  foet  are  there  in  a  plank  1 8  feet 
long,  12  inches  at  one  end  and  8  inches  at  the  other  ? 

Ans.  15  feet. 

12  +  8  =  20^2=10 


18  feet. 

9 
6 

15  Ans. 

(141) 


11-2  .\J  ENSURATION   OP   SURFACES. 

7.  How  many  square  feet  are  there  in  20  planks,  15  feet 
long,  and  each  9  inches  wide  ?  Ans.  225  feet. 

JVote.  When  there  is  a  number  of  planks  to  he  calculated 
of  the  same  length  and  breadth,  multiply  the  width  of  one 
in  inches  by  the  number  of  i^lanks,  divide  the  product  by 
12^,  and  multiply  by  the  length. 

9  X  20  =  180  ^  12  =  15  X  1^.=  225. 

8.  How  many  square  feet  are  there  in  50  pieces  of  scant- 
ling, 4  inches  by  3,  counting  "one  side  and  edge,  and  20  feet 
long?  Ans.  583^  feet. 

4  +  3  =  7  x50=350-H-12=:29ix20=583Heet. 

9.  How  many  square  feet  are  there  in  30  pieces  of  scant- 
ling 14  feet  long,  4  inches  by  2  ?  Ans.  210  feet. 


To  find  the  area  of  a  Triangle. 

Multiply  one  side  by  half  the  perpendicular  from  the 
opposite  angle. 

EXAMPLES. 


1.  If  A.  B.  be  65  poles,  and  the  per- 
pendicular 31  poles,  how  many  acres  are 
contained  in  the  Triangle  ?  ^^ — — (is^ 

31 4^  2  =  15  J  X  65  =  1007ipo.  or  6a.  Ir.  7^p. 

2.  How  many  square  feet  are  there  in  a  triangle  whose 
base  is  120  feet  and  perpendicular  75  feet?         Ans.  4500. 


To  find  the  circumference  of  a  circle  from  its  diameter. 

Multiply  the  diameter  by  3.14159;  or  multiply  the  dia- 
meter by  355,  and  divide  the  product  by  113. 


EXAMPLES. 


1.  If  the  diameter  of  the  earth  be  7930  miles,  what  is  the 
circumference  ?  Ans.  7930  X  3.14159  =  24912.8  miles. 


:.iE.NSURA'nON    OF    SUKi'ACKS. 


U^ 


2.  How  many  miles  does  tlic  earth  move,  iu  rcvohduir 
round  the  sun;  supposing  the  orbit  to  be  a  circle  whose 
diameter  is  190  millions  of  miles?  \urf  59G  OO'^  604 


!|     To  find  the  diameter  of  a  circle  from  its  circumference. . 

_  Divide  the  circumference  by  3.14150;  or  multiply  the 
circumference  ll;5,  and  divide  the  product  by  355. 

EXAMPLES. 

1.  What  is  the  diameter  of  a  tree  which  is  5.]  feet  round  ^ 

o    -r^,,      .         ,  3.14159)5.5000000(1.75  Ans. 

-..  it  the  circumference  of  the  sun  be  2.800.000  miles 

what  is  its  diameter?  ^^s^  891.2G7' 


To  ffid  the  area  of  a  Circle. 
Multiply  the  square  of  the  diameter  by  the  decimals  .7854. 

EXAMPLES. 

1.  What  is  the  surface  of  a  circular  lish-pond  which  is 
lO^^poIes  in  diameter?  lOx  lOx  .7854=^78.54  Ans. 

2.  What  is  the  area  of  a  circle  whose  diameter  is  623 

^^'t'  ,,  Ans.  304836. 

o.  How  many  acres  arc  there  in  a  circular  island  whose 

diameter  is  124  poles  ?  Ans.  75a.  76po. 


To  find  the  area  of  an  elipsis  or  oval 

Midtiply  the  longest  diameter  by  the  shorto^5t,  and  that 

product  by  7854. 

EXAMPLES. 


1.  What  ift  the  area  of  an  oval  who.<^e 
(greatest  diameter  is  36  feet,  and  least  28  ? 
—  -  -2BjiM>(  7854  =  791.68  feet  Ans 


144  MENSURATION    OF   BOLIDS. 

MENSURATION  OF  SOLIDS 

In  Bolid  measure  1728       cubic  inches =1  cubic  foot. 
282       cubic  inches =1  ale  gallon. 
'  231       cubic  inches =1  wine  gallon. 

150.42  cubic  inches=l  bushel. 

1  cubic  foot  of  pure  water  weighs  62  J  pounds. 

To  find  the  solidity  of  a  piece  of  hewn  timher,  box,  Sfc 
Multiply   the    length,   breadth,   and  depth   or  height, 

EXAMPLES. 

1.  How  many  solid  feet  are  there  in  a  piece  of  square 
timber  3  feet  by  2,  and  20  feet  long  ? 

3x  2 X  20=120  feet  Ans. 

2.  How  many  cubic  inches  are  there  in  a  piece  of  marble 
in  a  cubic  form,  which  is  12  inches  every  way  ? 

12x12x12=1728  Ans. 

3.  How  many  cubic  quarters  of  an  inch  are  there  in  one 
cubic  inch  ^  Ans.  64. 

4.  What  ia  the  solidity  of  a  wall  'J2  feet  long,  12  feet 
high,  and  2  feet  6  inches  thick  "^  Ans.  660. 

5.  How  many  cubic  inchcvS  are  there  in  a  box  2  feet  at 
the  bottom,*  3  feet  at  the  top,  4  feet  high,  and  6  feet  long  ? 

Ans.  108680. 


together 


To  find  the  number  of  bushels  or  gallons  contained  in  a 
corn-house  or  box,  ascertain  how  many  cubic  inches  are  con- 
tained ivt^the  box  or  house,  and  divide  them  by  the  number 
of  inches  in  a  bushel  or  gallon.  If  the  house  contain  ears 
of  com,  divide  the  number  of  bushels  by  2,  which  will 
I  give  the  number  of  shelled  corn. 

EXAMPLES-  * 

1 .  How  many  ale  gallons  are  there  in  a  cistern,  which  is 


-J 


In  all  such  ejcaniplcs  taice  the  average  width  or  length. 


MENSURATION   OF    30LIDS.  145 

11  feet  9  inches  deep,  and  whose  Ivasc  is  4  feet  2  inches 
square  ? 

.       f  The  cistern  contai  is  352500  cubic^  inches. 

^^'  I  And  352600  ^  2  ;2  =  1250  gaUons. 

2.  now  many  wine  gallons  wil  fill  a  ditch  3  feet  11 
inches  wide,  3  feet  deep,  and  462  f(  et  long  ?     Ans  40608. 

3.  How  many  bushels  of  corn  aie  there  in  a  crib  5  feet 
wide,  5  feet  high  and  10  feet  long, :  illed  with  ears  ? 

Ans.  IGObu.  lip.  -f 

4.  How  many  bushels  of  com  ar  >  there  in  a  cril  20  feet 
long,  10  feet  deep,  and  6  feet  wide '{  Ans.  '^81|.  -{- 1 

N'ote.  As  complete  accuracy  is  cot  to  be  expected  from 
any  rule  to  gauge  a  crib,  the  following  is  recommended  as 
being  accurate  enough  for  practice.  '  Multiply  the  number 
of  cubic  feet  in  a  crib  by  2,  and  d  vide  the  product  by  5. 
Take  the  above  example, 

2  X  10  X  6  =  1200  X  2  =  2400  -rf  5  =  480. 

5.  How  many  bushels  of  com  ar.?  there  in  a  crib  16  feet 
bag,  10  feet  high,  8  feet  wide  at  tha  bottom,  and  6  at  the 
top?  Aia.  480. 

6.  How  many  bushels  of  coal  wlI  a  coal  bed  contain,  14 
fijat  long,  4  feet  wide,  and  3  feet  6  mches  high  ? 

AnB.  166^^. 

Ab/c,     In  suob  examples,  it  will  produce  very  near  the 
true  result  to  multiply  the  number  Df  cubic  feet  bj  4,  ani[ 
divide  the  prodtiot  by  5. 


To  mate  a  box  large  enough  to  c  mtain  a  given  fpiantity, 
multiply  the  number  of  bushels  or  ;^11ods  to  bo  contained 
by  the  number  of  cubic  inches  in  a,  bushel  or  gallon.  If 
the  box  is  to  be  in  a  cubic  form,  extract  the  cube  root  of  the 
product.  If  the  side  or  end  of  the  box  be  given  to  ascer- 
tain how  long  or  wide  it  must  be,  d  vide  the  product  by  the 
number  of  square  inches  contained  oj  the  side  or  end. 

EXAMPLES. 

1.  It  is  required  to  make  a  box  in  a  cubi«  form  krgo 


;146  MENblJRATION    OF    SOLIDS. 

enough  to  contain  1  bushel.     How  many  inches  must  it  be 

every  way  ? 

The  cube  root  of  2150= 12.9  i-  in.  inako  it  18  in.  every  way. 

2.  How  large  a  box  in  the  form  of  a  cube  will  contain** 
I  bushel?  Ans.  10.29  4-  or  lOi  in.  nearly. 

3.  How  large  a  box^  in  a  cubic  form,  will  contain  5 
bushels  ?  Ans.  22  -f  in. 

4.  How  long  must  a  box  be  made  to  contain  60  bushels, 
which  is  to  be  4  feet  wide  and  3  feet  high  ? 

Ans.  5  feet  2.2in. 
2150x50=:=107500-r-172S=62.2==5ft.2.2in.36x48=^1728 

5.  What  must  be  the  length  of  a  box,  the  end  of  which 
is  3  feet  by  2,  to  contain  20  bushels?         Ans.  5  feet  l|in. 

6.  How  wide  must  a  box  be  made,  which  is  to  be  10  feet 
long  and  5  feet  deep  ?  Ans.  4  feet  11.72  in. 


To  Jind  the  iolidity  of  a  Cylinder 
Multiply  the  area  of  one  end  by  the  length. 

EXAMFLLB. 

1.  What  is  the  solidity  of  a  cylinder  whose  length  is  60. 
I  inches  and  diameter  20  inches  ? 

20  X  20=400  X  .7864=3141600  X  60=18849.6  Ans. 
What  is  the  solidity  of  a  cylinder  whose  length  is  121 
;inchea  and  diameter  45.2  inches?  Ane.  194156.6. 

j     3.  The   Winchester  bushel  is  a  hollow  cylinder  18  J 
inches  in  diameter  and  8  inches  deep?  Ans.  2150.42. 

'     4.  How  many  cubic  feet  are  there  in  a  log  of  timber  2 
•feet  in  diameter  and  20  feet  long?  Ans.  62.83. 

5.  A  gentleman  has  a  bushel  measure  which  is  15  inches 
in  diameter  and  12  inches  deep,  how  much  is  it  too  great  or 
too  small?  Kn<^  i  29.84  inches,  or  a  little  more 

'"I  than  a  pint,  wine  measure. 

6.  A  gentleman  has  purchased  a  gallon  measure  in  the 
fonn  of  a  cylinder,  which  is  6  inches  in  diameter  and  10 
inches  deep.  He  was  told  it  was  a  wino  measure  by  the 
merchant.     Is  it  a  correct  measure  ? 

,        f-It  ^ontaaib  282.7  cubic  inches: 
"^  ^  *  '  therefore  it  must  l>e  ale  mearave. 


GAUGING    OF   CASKij.  147  i 

Tojind  t/ie  contents  of  a  vessel  in  the  shape  of  a  frustrum 

of  a  cone. 

Square  tlie  diameter  of  each  end,  multiply  tlieir  squares 
together,  and  extract  the  square  root  of  their  product,  to 
which  add  the  two  squares,  and  then  multiply  by  the  deci- 
mals .7854  and  i  of  tho  length. 

EXAMPLES. 

1.  How  many  cubic  inches  are  contained  in  a  vessel  9 
inches  deep,  4  inches  in  diameter  at  the  bottom,  and  3  feet 
at  the  top  {  Ana,  87.18  cubic  inches. 

4  X  4==16     3  X  3=9  X  16=144  the  square  root  is  12 
9^16-fl2rrr37x. 7854=29.0598x3=87.13  cubic  in. 

2.  A  measure  which  has  been  made  for  a  wine  gallon  is 
6  inches  at  the  bottom,  5  inches  at  the  top,  and  10  deep. 
Is  it  a  correct  measure  ? 

.        f  It  contains  238  cubic-inches,  7  cubic 
*  (  inches  too  much,  or  1  gill  nearly. 

3.  A  measure  which  has  been  made  to  contain  ^  bushel 
is  12  inches  at  the  bottom,  15  inches  at  the  top,  and  15 1 
inches  high.     Is  it  a  correct  measure  ? 

Ans.  It  contains  1019- 7  cubic  inches,  56  too  little. 

4.  How  many  gallons,  wine  measure,  will  a  large  crout 
tub  contain,  9  feet  high,  4  feet  at  the  bottom,  and  3  at  the 
top?  Ans.  87.18  cubic  feet,  or  652.15  wine  gallons. 


GAUGING  OF  CASKS. 

There  are  commonly  reckonod  four  varieties  of  casks,  for 
eflxjh  of  which  some  have  a  different  rule,  but  the  following  t 
I  rule  will  apply  to  all : 

To  calculate  the  contents  of  a  cask,  reduce  tlie  dimensions 
Ito  inches;  subtract  the  head  from  the  bung  diameter,  multi- 
jply  the  difference  by  the  decimal  .7,  if  there  be  much  curve 

;of  the  .staves  betwixt  the  head  and  bung,  by  .67,  if  a  little 
jmore  than  common,  .6,  if  common,  .57,  if  but  little,  .52,  if 
jnonc.     To  this   product   add  the  head  diameter.     Square 

'  "-  '•■  "■•  •' •■  '--  -  •  •■■"'^ '  •   ■   •  ^  '' 


jT?  •T. 


1248  TONNAQ.i  or  FLAT  BOATS. 

their  suia,  which -mul tip' j  by  the  decimals  .0028,  when  ale^, 
aiid  .0024,  when  wine  giUons  are  required,  and  the  length 
of  the  cask. 

A^ote.  .0028  and  Ml  4  are  the  results  of  dividing  .7854 
by  282  Lnd  231. 

:XAMPLE8. 

1  W  lat  is  the  capaciij  of  a  cask  which  has  much  -curve 
b(  twixt  ohe  head  and  I  ung,  30  inches  long,  head  diameter 
18,  and  bung  24  inches  1' 

Ais.  60.26  wine,  or  41.3  ale  gallons. 

24— 18r=6x  7=4.2 -f  J  8=22.2 x  22.2=4928.84  x  .0084 
=  16.75656  X  30=50.239680  gnllons. 

2.  How  many  wine  j;.allons  will  a  casl^  contnin,  of  com- 
mon curvature,  which  i,-  30  inches  long,  head  diameter  18, 
and  buu;^  24  iiiches  ?  Ans.  45.9  gallons. 

8.  What  is  the  capac}vj  of  a  cask  without  curvature  be- 
twixt thi)  head  and  bung,  30  inches  in  length,  head  diameter 
13,  and  oung  24  inches  ' 

j\.nB.  37.3  ale,  or  45.3  wine  gallons. 

4.  Hew  many  wine  gallons  will  a  cask  contain,  of  the 

Jc^mmon  form,  whose  lei  gth  is  27  inches,  head  diameter  21, 

and  bun*,'  23  inches  ?  Ans.  46.24  gallons. 


TONNAGi:  OF  FLAT  BOATS. 

The  quantity  which  any  vessel  will  carry  is  equal  in 
weight  to  the  quantity  of  water  which  the  vessel  displaces 
by  loadi?igj  therefore  tha  number  of  cubic  feet  of  water  dis- 
placed b7  loading  a  ves^^l,  multiplied  by  62^,  will  give  the 
number  of  pounds  whic  i  that  vessel  will  carry. 

To  aj' certain  how  m;ny  tons,  barrels,  &c.,  of  %  certain 
(weight,  a  Flat  Boat  will  carry 


TONNAGE  or  iXAV  BOATS;  149 


RULE. 


Subiraot  ^  the  lake  or  rakes  tiv  a  the  length.  Multiply 
the  remainder  by  the 'depth  to  wiich  she  is  suik  by  the 
load,  and  that  product  by  the  width  measured  'a*om  the 
outside  of  the  gunnel.-^.  If  the  pi  oduct  is  not  ir  feet,  i-e- 
duce  it  to  f^Qt,  which  multiply  by  52^,  which  will  give  tlje 
number  of  pound?,  which  reduce  to  tons,  or  divicie  by  the 
I  weight  of  a  barrel,  &c. 

JEX^lMPLES. 

t      1.  How  much  will  a  flat  boat  c*a:ry  which  is  50  feet  long, 
'rake  10  feet,  12  feet  wide,  and  wil   bear  sinking  1|  feet? 
I  Ans.  22  tons  12  e\t 

i50  —  5=r:45X  l^r:::67^V  12=:81C  X  62A:r=  50625  ^112  rn 

452-20=22  ton.  12  cwt. 

2.  What  number  of  flour  bai-rels;  which  weigh  IC  6  pounds 
each,  will  a  flat  boat  carry  which  i?  capable  of  being  suik 
1  foot  3  inches,  50  feet  long,  one  lake  10  feet,  tho  other  8 
f(yA,  15  foot  wide?  Ans.  515. 


r^>ii,iin   irfiii,      mil    I   inn    l»»»j* 


TABLES. 

Of  the  present  state  of  real  and  imaginary  monies  of  the 

most  commercial  parts  of  the  world,  with  tlie  United  States, 
and  reduced  to  the  value  of  the  monies  thereofjin  Dollars, 
Cents  and  Mills, 

This  mark  t  is  prefixed  to  the  imaginary  moiicy«  or 
money  of  account. 

This  mark  ::=  is  make,^  or  equal  to. 

In  the  column  of  Mills,  wherever  a  tij^are  is  preceded  by 
a  point  {.)  it  coni'crta  it  to  decimals :  I'hus  6.8  means  $ix 
mills  and  eight-tenths  of  a  mill. 


A-miBMlCA, 


UNITED  STATES, 


A 

5  i\lills  =  a  half  cent . 

10  Mills        a  cent^ 

S^Centg       a  half  dime 
2  Halfdimesa  dime  .. 


25 
50 
10 
'2\ 
5 
10 


Cent^ 

Cents 

Dimes 

Dollars 

Dollars 

Dollars 


a  I  of  a  dollar 
a  half  dollar   . 

a  dollar 

a  4  eagle  .... 
a  1  eagle  .... 
an  eagle 


Doils.  jCentB.l  Mills. 


1 

2 

5 

10 


1 
5 

10 

I  25 
50 

50 


Accounts,  in  the  United  Statps^  are  kept 
in  Dollars  and  Cents. 

CANADA,  NCn^A  SaJTlA,  &c. 


A  "fFarthing . . 

4  Farthings  =  a  penny  . 
12  Pence  a  shilling* 

60  Pence  a  dollar. . 


1 

20 


4.1 

6f 


(i^C) 


TABLES   or   iOREIGN    MONEY. 


15) 


CANADA,  NOVA  SCOTIA,  ^c. 

(continued.)  * 

20  Shillings  =^  a  pound 4 

30  Shillings        a  moidore '  6 

40  Shillings       a  half  Joe |  8 

50  Shillings       a  Federal  Eagle 1  10 

AccouatK  are  kept  in  pounds,  shillings^! 
and  pence;  but  they  are  also  kept  in  some  | 
parts  of  Canada  in  IJvres,  sous,  and  deniers,  ; 
according  to  the  ancient  system  of  France,  | 
and  is  called  Old  Currency. 


MEXICO,  PERU,  CHILI,  kc. 

5iE^Accounts  are  kept  here, and  all  other 
partj:  of  Spanish  America  in  Pesos  and  Dol- 
lars of  8  ideals,  the  Real  being  divided  into 
halves  and  quarters;  this  Real  is  occasion- 
ally divided  into  IG  parts,  and  ?'iSO  into  34 
51arf,vedis  of  Mexican  plate. 


DollH.  iceuts.JMill/ 


BRAZIL. 

Account*  are  kept  here  u^  in  Portugal,  in 
jReas,  1000  making  the  Milrea;  100,000 
I  being  100  milrcas;    and   1.000,000,  one 

thwii»and     Milreas,   commonly    called    n 

Con  to  of  Mih-cas. 


:sti»OPJ3. 

.NOKUifcttN    PAKT8. 

ENGLAND  AND  .SCOTLAND.        ; 

LomJov,  lAirrpcoI,  .Bristol,   Edinhnnj^  t 
Glasaow,  (f!:c.  ! 


!        A  fEarthing 

I    2  Farthings  ~-  a  halfpenny 
j    2  Halfpence      aj.enny... 


4.( 

8* 


mtmmmamtan 


ngTW  IT  BtrwirtafigUJ 


TABLES  or   FOREIGN   MONEY. 


nl 


ENGLAND  AND  SCOTLAND.       | 
(continued.)  i 

4  Pence     ~  a  groat , 

6  Pence  a  half  shilling 

12  Pence  a  shilling  .  = 

54  Pence  an  American  dollar  .,.,*. 

5  Shillings      a  crown   

20  Shillings      a  ^ound  sterling  ....... 

2 1  Shillings      an  English  guinea 

Accounts*  are  kept  in  Pounds,  Shillings, 
Pence,  and  Farthings. 

jYote.  AUhoiigh  the  English  crown  at 
the  par  of  exchange  is  $1.11  1 . 1,  yet  in 
the  United  States  it  passes  only  for  $i  10 
cents,  and  the  gold  coins,  instead  of  passing 
at  their  par  value,  are  now  regulated  by  the 
rate  of  exchange  between  the  two  countries. 

mELAND. 

Dublin,  Cork,  Londonderry ^  Sgc. 

A  fFarthing 

2  Farthings  =  a  halfpenny 

2  Halfpence      a  penny 

12  Pence  a  shilling 

13  Pence  an  English  shilling . . . 
58 1  Pence            an  American  dollar  , . . 

20  Shillings        a  pound 

22|  Shillings        an  Englbh  guinea  . . . 

Accounts  are  kept  in  Pounds,  Shillings, 
Pence,  and  Farthings. 

BREMEN. 


Dolls.  I  Cents 


MiliB. 


7 
\  11 
22 

11 
44 
66 


4 

1.1 

2.2 

1.1 
4.4 
6.7 


A  tPfening 

IJ  2  Pfennigs  =  a  sware 
5  Swares  a  grote 


4.3 


t  iipi  ■ 


TABLE3    OF   POllEIGN    MONEY. 


163; 


BREMEN.— (coxTixNUED.) 

3  Grotes    -^  a  double  shilling 

24  Grotes         a  mark 

48  Grotes         u  double  mark 

72  Grotes  or 

3  marks      a  tdxdollar 

Accounts    arc  kept  in   Kixdollahs   and 
Grotes. 


Dc  /<». 


HANOVER. 


A  jPlcnii)^, 

3  Pfenings  ~ 

8  Pfenings 

12  Pfenings 

8  Groshen 

16  Groshen 

24  Groshen 

32  Groshen 

34  Groshen 


a  dreyer 

a  marien 

a  tgrosh  

a  half  guilden  .......... 

a  guilden 

a  |rixdollar 

a  double  guilden 

a  ducat 


Accounts  are  kept  in  RixdoUars,Groshen, 
land  Pfening-s. 


AUSTRIA  AND  SVVABIA. 

Vienna^  IHes^^  jlugslnirg,  Blenh$im,  Sfc 

A  |Phening 

2  'Phenings  ~  a  dreyer 

4  Phenings        a  |creutzeir 

14  Pheuingd        a  grosh , 

4  Creutzers       a  batzen 

1 5  Batzen  a  |gould  or  f  florin  .... 
iK)  Creutzerg       a  rixdoilar 


C  nl8. 

3 
25 

51 

76 


'  2 

3 
26 
52 
78 

5 
10 


3 

3 

52 

78 


!«<SS 


2.  V 

4 

H 

5 
ft 


io^i 


TABLES    OF    FOREIGN    MONT.Y. 


AUSTRIA  AND  SWABIA. 
(continued.) 


30  Batzen  =  a  specie  dollar' 
60  Batzen       a  ducat 


Doils. 


Cents. 


5 
10 


Accounts  are  kept  in  Florins,  Creiitzers, 
and  Phenings.  j 

! 

•Although  the  par  of  exchange  makes  a  j 
specie  dollar  1  dollar  and  5  cents,  yet  lu 
the  United  States  it  is  worth  but  a  dollar. 


OLLAND  AND  ZEALAND, 

Sinstcrdairij  RoUerdam,  Middleburg  and 
Flushing. 

A  "j  Penning 

8  Pennings  =:=  a  gwte 

2  Grotes  a  f stiver 

6  Stivers 

20  Stivers 

50  Stivers 

60  Stivers 

105  Stivers 

6  Guilders 


a  seal  in 
a  Iguilder  . . . , 
a  rixdollar . . . . 
a  drey  guilder 

a  ducat , 

a  pistole  ,  .  . , 


Accounts  are  kept  in  Guilders,  Stivers, 
*nd  Pennings. 


SOUTHERN    PARTS. 

PORTUGAL. 

A  -fRm 

10  Rcas      «=ft  half  vintin. . . 

20  Reas  A  viatin 

5  Vintias      a  teetoon 

'—^-"—T-  II  ]    '     i7~i      Ml  I 


1 

2 

12 

40 

1 

1 

20 

2 

10 

2 

40 

1 

2 
V2 


niimii^friii  t\iu 


TABLES   or   rOREIGN    ^lONEY. 


156 


PORTUGAL.— (continued.) 

4  Ti'stooDs  ==:  a  crusad  of  exchange. . 

24  Vmtins  a  new  crusado 

10  Testoons        a  "fmiilrea 

48  Testoons        a  moidore 

64  Tjstoons        a  Johannes 


Accounts  are  kept  in  Millreas  and  Reas. 


FRANCE  AND  NAVARRE. 

Paris,    Lyonsy    Marseilles^    Bardeaux^ 
\  Baycmne^  S^c. 

I  A  teenier 

I   3  D  rniers  ^-^  a  hard 

i    2  Liards  a  dardene 

:  \2  Deniern  a  j&ol 

j  20  Sols  a  tlivre  tournois 

'■  60  Si-ls  an  ecu  of  exchange 

I   0  Livres  s.n  ecu  or  crown 

1 10  Livre^-  a  pistole 

1 24  Livres  a  Louis  d'or   

! 

I     Accounts  are  Icept  in  Livres,  Sous,  and 
P«niers. 

j     Since  1795  accounts  are  kept  in  Fiance 
I  of   10  Decimes  or  100  Centimes.     The 
J  Livre  and  Franc  were  formerly  of  tlie  same 
value:  but  by  a  decree  of  1810,  the  follow- 
,  ing  proportion  has  been  established  : 
Pieces  of  48  Livres  at  47f.  20c. 
of  24  £t  23  .  55 

of    6  at    5  .  80 

of^  3  &t    2  .  75 

The  modern  .^^olJ  coins  are  Napoltons 
of  40  and  20  Fraiics,  and  Louis  cf  tli© 


Dolls. 

Cents. 

50 

60 

1 

25 

6 

8 

! 

! 
1 

18 

1 

55 

i     1 

11 

1 

86 

!     4 

44 

* 

1 
1 
1 

Mills. 


2.3 
4.6 

H 

5 
6 
1    i 

4.4 


tftn»»ra«a— »  *itf»Lliwiii  ■ 


— w»— I  nm^iiii^i 


156 


TABLES   OF   FOREIGN    MONEY. 


JVote.  French  crowns  at  the  par  of  ex- 
change are  estimated  at  1  dollar  111.1 
cts.,  but  they  only  pass  for  1  dollar  10  cts. 


SPAIN  AND  CATALONIA. 

Madrid^  Cadiz,  Seville^  Sfc. 

NEW   PLATE. 

A  f Maravedi , 

2  Maravedis  =  a  quartit 

*34  Maravedis       a  |Real 

2  Reals  a  pistareeii 

8  Reals  a  piastre  of  exchange 

10  Reals  a  tdollar 

375  Maravedis  a  ducat  of  exchange  . 

32  Reals  a  pistole  of  exchange 

36  Reals  a  pistole 

Accounts   are  kept  in  Dollars,  Reals, 
and  Maravedis. 


Dolls. 


Gibraltar*  Malaga,  Denia^  6$c, 

VELON. 


4 

34 
15 
512 
GO 
2048 
70 


A  fMaravedi 
2  Maravedis 

Maravedis 

Maravedis 

Reals 

Maravedis 

Reals 

jMaravedis 

Reals 


an  ocnavo  .... 

a  quartil 

a  treal  velon  . . 
a  f piastre  of  ex. 

a  piastre  

a  pistole  of  ex. 
a  pistole  of  ex. 
a  pistole 


Account   are  kept  in  Doilars,  Reals^. 
and  lilaravsdis. 


Cents.  Mills. 


10 
20 

80 

10 

18 

72 


79 
79 
18 
.18 
72 


2.9 
5.8 


as 


att; 


TABtiES  OF  FOREIGN    MONEY. 


167 


BarceloTUty  Saragossa,  Valencia,  Sfc, 

OLD    PLATE. 

A  t Maravedi 

16  Maravedis  =  a  soldo 

2  SoldoB  a  "frial,  old  plate 

16  Soldos  afdollar 

20  Soldos  a  libra. 

24  Soldos  a  ducat 

60  Soldos  a  pistole ........... 

There  are  also  Ducats  of  21  aid  22 
Soldos. 

Accounts  are  kept  in  Dollars,  Reals 
and  Maravedis. 

JS*ote. — Although  60  Soldos  are ecual  to 
3  dollars  and  75  cents,  the  Spanish  Tistole 
is  worth  but  3  dollars  and  60  cents 


ITALY. 
Genoa,  JVowt,  4rc.,  Corsica,  Baska^  Sfc, 

A  fDenari .- 

12  Denari  =  a  "fsoldi 

4  Soldi  a  chevalet • .    .... 

20  Soldi  '        a  flira 

30  Soldi         a  testoon 

5  Lires  a  croisade 

115  Soldis        a  pezzo  of  exchange. .. . 

6  Testoons  a  genoine .... 

20  lires  a  pistole 

Accounts  ai'fi  kept  in  Lires,  Soldis,  and 

Denaris. 


DollB. 


C«nts. 


. 


Leghorn^  Florente,  4r** 

A  jDenari 

4  Denaris  =  a  quatrini 

14 


6 
12 

25 

50 
60 


a 

15 
23 
79 
92 
44 
18 


168 


TABLES   01    FOKEiaN   MONEY. 


ITALY,  &.C.— (continued.) 

12  Denaris  =  a  |Soldi 

5  Quatrinis     a  craca 

a  qiiilo 

a  jlira 

a  piastre  of  exchange  .  . , 
a  ducat 


18  Cracad 
20  Soldi 
6  Lires 
7J  Lires 
22  Lires 


Dolls. 


a  pistole  .............  j     3 


Accounts  are  kept  in  Liresj  Soldisy  and 
Denaris. 


ASZJL 

BENGAL. 

Calcutta^  Callictttj  Sfc, 

A  [Pice •  . . . 

4  Pices  =  a  fanum 

6  Pices       a  viz 

12  Pices       an  ana 

10  Anas        a  piano 

1 G  Anas        a  rupee 

2  Rupees  a  French  ecu  or  crown  .... 

2  Rupees    an  English  crown 

56  Anas        a  pagoda  . 

A  Lack  IS  100,000  rupees. 

Accounts  are  kept  in  Rupee^^  Anas,  and 
Pice. 


CHINA. 

Pekin,  Canton^  ^c. 

A  jCash 

10  Cash      =  .  a  fcandareen 

10  Candareens    a  f  mace 

10  Mace,  1  oz.  6  dwt.  16  grs.'=  a  ftale 

Accounts  arc  kept  here  in  Tales,  Mace, 
;|  Gandareen?.  and  Cash. 


Cents. 


Milts. 


1 

10 
15 
92 
15 
44 


j7.7 
i2.8 
2.8 
4.3 
5.9 
7.3 
14*.  4 


1 
1 
3 
34 
55 
11 
11 
94 


1 
14 

48 


2.9 
1.6 
7.3 
4.7 

6.8 

1.1 
1.1 

4.4 


1.4 

4.8 
8 


BBUSBi 


kMMWaateAM 


iTtsni 


TABLES   OP  FOREIGN    MONEY. 


159? 


MocJia. 

A  tCarat 

6  Carats     =     a  commarsee 

Carats  a  | caveer 

Commarsees  a  cofTala 

Coflalas  a  fMocha  dollar 

Mocha  Dollar  a  Spanish  Dollar 

Coffalas  a  sequin 

Sequins  a  tomond , 

)Vecounts  are  kept  in  Piastres  or  Mocha 
Dollars,  and  Caveers. 


ISLAND  OF  JAVA. 

Batavia. 

A  tDoit 

4  Doits    =    a  Istiver 

8  Doits  a  cash  or  dubbettjees  . , . 
3  Doits  a  satalie  or  schilling  .... 
3  Satalies        a  sooka 

9  Cash  a  sooka  satalies 

15  Cash  a  current  rupee 

24  Cash  a  fPardaoor  rixdollar  . . . 

60  Stivers  a  dollar 

13  Schillings  a  ducatoon 

J^ote, — A  new  system  of  monies  has 
been  established  by  the  king  of  the  Nether- 
i  lands. 

The  unit  is  the  new  Gulden  or  Florin 
of  the  Netherlands,  and  instead  of  decimal 
divisions  is  divided  into  4  Schillings,  12 
Dubbels,  24  Dutch  Stivers,  30  Indian  Sti- 
vers, or  120  Doits. 


DoUfl. 


Cents. 


MilU. 


1 
1 

15 


1 
1 
6 
"83 

66 


1 
1 
10 
20 
30 
50 
80 

30 


160 


VABLES   OS  FOREIGN    MONEY. 


Isle  of  jBourhoHy  and  Isle  of  France. 

A  Denier  . ». ,  , 

12  Deniers  =  a  "fSoiis 

20  Sous  a  flivre 

IQ  Livre*         a  dollar , 


EGYPT. 

Old    and    JSTm     Cairo^    Mexandria^ 
Sttyde,  Sfc. 

An  |A«per 

3  Aspers  =  a  tmedino 

24  Medini       an  Italian  ducat. 

80  Aspers       a  piastrs ._. 

30  Medini       a  dollar 

96  Aspers       an  ecu 

32  Medini       a  crowii 

200  Aspers       a  suttaiiin 

70  Medini      a  Parzo  dollar 

Accounts  are  kept  ia  Piastres,  Medini, 
and  Aspsis. 


iBARBARY. 

JilgieTSy  TimiSj  Tripoli^  Una,  ^c. 


Bolls. 


Cents. 


An  f  Asper , 

3  Aspers  =  a  mediuo 

10  Aspers       a  reai^  old  plate 
a  fdoul  le   .... 

a  doUai 

a  silver  chequin 
a  dollai 


2  Reals 

4  Doubles 

24  Medini 

30  Medini 

180  Aspers 

15  Doubles 


a  zequiJi 
a  Pisto.^  e 


Accounts  are  kept  in  Doubles  and  Aspers. 


10 


1 
3 

74 
88 

10 
10 
22 
33 


1 

3 

12 

25 

74 

9G 
72 


Mills. 

0.4 
5 


0.3 

0.8 

9 


TABLES  or  roiiiiil?!*^  MdpSrE-ir: 


Igi 


WBST  INDIES. 

Jamaica  and  Bermudas. 

A  Farthing 

4  Fanhiug  =  a  "jpeiiny 

1\  Pence  a  real  or  bit 

2  Bits  a  pistereen 

12  Pence  a  t-shilling 

20  Pence  a  J  of  a  dollar  ....... 

80  Pence  a  dollar 

1 6  Shillings        a  half  English  guinea  . 

20  Shilling.';        a  tpound 

40  Shillingij        u  moidore 

53^  Shillings        a  half  joe,  I)  dvvt 

Accounts  are  kept  in  Pounds^  Shillings, 
and  Pence. 

JVo/e.— -As  the  currency  of  JTamaica  ,is 
1 .407.,  its  proportion  to  sterling  is  as  7  to 
5.  Hence  \l.  sterling  =  17.  85.  currency; 
and  U.  curreycy  —  145.  3J«7.  sterling. 


Barhadoes. 

A  Farthing 

4  Farthings  =  a  penny 

7  J  Pence  a  real  or  bit 

2  Bits  a  pistareen 

12  pence  a  shilling 

75  Pence       ,       ^  dollar. 

20  Shillings         a  pound 

27j  Shillings         a  moidore 

50  Shillings        ,u  half  Joh{innea  ...... 

.  A<'-covsiUs  are  kept  in  Pounds,  Shiliings, 
Pence,  aud  Farthincrs. 


Dolls.   Cents.  Mills 


1 

10 

20 

15 

'25 

33 


1 
10 
20 
IG 

20 


i6-2 


TABLES   OF   rOEEIGN   MONEY. 


Bafiamas. 


A  f  Fiirthuig 


4  Fanhiiigs  =:=  a  fpcnny 


0  Pence 
12  Pence 
90  Pence 
20  Shilllrigs 
48  Shillings 
64  Shillings 


a  bit 

a  "fshiiling   .  , . . 

a  dollar 

a  tpound   . . . . . 
a  nioidore    . . .  . 

a  half  Johanncjs 


DolU. 

Cents. 

Mills.  1 

• 

2.6 

1 

10 

04 

12 

5 

1 

3 

6 

• 

8 

Accounts  are  kepi  in  Poundis.  Shiiihigs, 
Pence,  and  Farthings. 


Sl    Barthohmews,     St.    Kitts^    JSTevis, 
Antigua  and  Montserrat, 

A  fFarthing , 

4  Farthings  ~  a  tpenny  

9  Pence  a  bit 

12  Pence  a  jshilling 

8\  Shillings         a  dollar  . , 

1 1   Bit?  a  dollar 

20  Shillings         a  fpound 

66  Shillings         sl  half  Johannes 

Money  of  account,  Pounds,  Shillings, 
Pence^  and  Farthings. 


Dominica^    St.    Vincents^    Grenada^    St. 


A  fFarthing 

4  Farthings  =  a  |penny  . 

9  Pence  a  bit  ... . 

12   Pence  a  fshilling 


I 

9 
12 


40 


n 


8 
11 


2.3 

H 

3.3 
1.1 


"•■(W 


l^^^^^lhMMM 


;v;-t^'   g; 


«i  >-iii"'1  Ttit  r  rt WJm  III    I  At  III  ■■»»»<—>1rteifc& 


TABLES   or   FOREIGN   MONEY. 


163] 


Dominica y  Sfc.  (continued.) 


13  Bits         =  a  dollar . 
20  Shillings      a  fpound 


Dolls. 


Accounts  are  kept  in  Pounda,  Shillings, 
Pence,  and  Farthings. 


Martinique,  St.  Lucia,   Guad^tloupCy  Sfc, 

A  Denier 

13  Deniers  =  a  sol 

15.  Sols  an  escalin 

20  Sols  a  livre 

3  Escalms       a  J  gourde 

9  Livres  a  piastre  gourde  ..,.,.. 
12  Escalins       a  piastre  gourde 

8  Gourdes       a  J  Johannes,  9  dwts. . . . 

J  of  a  Quadruple  =  4  dwts.  6  grs 

J  of  a  Quadruple  8  dwts.  12  grs.  . . 
A  Quadruple  17  dwts 

jMoney  of  account,  Lirrcs,  Sols,  and 
Deniers. 


St,  Domingo,  (Spanish  part,)  CuhOf  Porto 
Rico,  Sfc, 


A  Cluarter  Real 

A  tHalf  Real 

4  Quarters  3=  a  freal ' 

2  Reals  a  Peso  Medeo  . . 

4  Reals  a  jpeso  or  dollar 


Accounts  are  kept  in  Pesos  or  Dollars* 
Reals,  and  Half  Reals. 


1 
1 
8 
4 
8 
16 


Cents. 


Mills. 


22  12.2 


8 
11 
25 


3 

6 

12 

35 


Oi 

H 

1.1 


H 

5 


I II m     II    n 


fi04 


TABLES   OF   FOREIGN    MONEY. 


St.  Domingo,  (French  part.) 

In  the  French  part  of  St.  Domingo  or 
Hayti,  accounts  were  formerly  kept  in 
Livres,  Sols,  and  Deniers  current;  and  the 
Dollar  was  then  reckoned  at  8  Livres  5 
Sous  current;  but  at  present  accounts  are 
mostly  kept  in  Dollars  and  Cents,  as  in 
the  United  States. 


Si.  Emiaiia^  St,  Martin^  Curaqoa,  S;c. 

A  Farthing 

4  Farthings  =  a  |penny 

9  Pence  a  bit 

12  Pence  a  fshilling , 

8 1  Shillings         a  dollar  ....    ....  ...^,, . . 

11  Bits  a  dollar '..'*.  ... .. 

20  Shillings        a  fpound 

Money  of  account,  pounds,  ShiUingSj 
Pence,  and  Farthings. 


St.  Thomas^  St.  Johriy  Santa  Cruz. 

A  jStiver 

5  Stivers  =  an  old  Bit 

6  Stivers       a  jgood  bit 

8  Good  Bits  a  fpiece  of  I 

12^  Good  Bits, 

or  15  Old,  a  dollar  ........ , .,. . . . 

75  Good  Bits  a  moidore  . . .  .'i';-;*/  ..V". 

100  Good  Bits  a  half  joe A  9tK 

'     Accounts  are  made  out  in  Pieces  of  f^ 
iBits,  and  Stivers. 


Dolls. 


Cents. 


Mills 


1 

9 
12 


40 


H 


I 

8 
64 


3^ 

61 


■■!■  ■■■   I  J  ■ 


TABLES   OP   FOREIGN    MONEY. 


1G5 


Surinam,  Berhice,  Demerard,  Sfc. 

A  fDiiit 

1 G  Duits     ;r=  a  stiver 

20  Stivers        a  guilder , . , . 

2i  Guilders      a  dollar 

5  Guilders      ^  Johannes 

1 5  Guilders      a  moidore 

20  Guilders      a  half  Johannes   

Accounts  are  kept  in  Guildei*s,  Stivers, 
and  Duits. 


Canary  and  Madeira  Isl({^ds. 

A  tHce 

62|  llees  =  a  sixteenth  of  a  dollar  . . . 

62|  Rees        J  of  a  pistareen 

125  Rees        |  of  a  dollar 

125  Rees        J  of  a  pistareen  ........ 

250  Rees        J  of  a  dollar 

250  Rees       a  pistareen 

1000  Rees       a  milree 

Accounts  are  kept,  a?  in  Portugal,  in 
Rees  and  Milrees. 

JVo/ff.-T.A   pistareen,  which  is   wortli 
I  only  20  Cents,  passes  in  Madeira,  the  same 
as  a  quarter  of  a  Dollar,  which  is  worth 
25  Cents 


Dolls. 


Cents. 


Mills. 


3 

40 


lii 


6 
5 
12 
10 
25 
20 


2i 


??s_    ^    ■  ■■ ..  -  . ii:ij.>j^^ 

SHORT  METHOD 

TO 

CALCULATE  INTEREST. 

RULE. 

Multiply  the  sum  by  half  the  number  of  days,*  that  pro- 
duct being  divided  by  30  will  give  the  interest  in  cents. 

EXAMPLES. 

V  ^at  is  the  interest  of  165  dollars  for  16  days. 
165  dollars 
8  half  the  number  of  days 

30)1320(44  cents 
120 


120 
120 


REDUCTION  OF  COINS. 

Tl  e  Dollar  having  different  denominations  of  value 
throrghout  the  United  States,  some  simple  rules  for  re- 
ducirg  the  respective  nominal  values  to  Dollars  and  Cents 
may  not  be  unacceptable. 

The  Dollar  is  valued  at  6  Shillings  in  the  states  of  New 
Hampshire,  Massachusetts,  Rhode  Island,  Connecticut,  Y^^^" 
,  ginia,  Kentucky,  and  Tennessee. 

To  reduce  the  Currency  of  these  States  to  Dollars  and 
Cents,  take  this 

RULE. 

Add  a  cypher  to  the  right  hand  of  the  pounds,  and  divide 
*  Counting  360  days  in  a  year. 


KKDUCXIUN    or    C^Jl.NS.  ItiT  i 


by  3,  the  quotient  will  I)o-dollarf^— If  there  are  sbillinga  io 
I  the  sum^  ud-i  1  dollar  5or  every  G^*. 


KXAVi'J^fc.s.. 


1 .  Kedxioe  lOiil  t>  vl<>llar6  aud  otuts. 


o^ 


Keducc  4t>.^.  1;')^.  Ikl  to  dolbn;  :iud  centa. 
3>i60 

15o.o3^ 


Ansv/er  6155.96  acarly. 

The  Dollar  U  valaod  at  7^.  OrZ.  ia  the  States  of  Pennsyl- 
vania, New  Jcrt?ej,  Mary knd,.  and  I>elaware;  to  reduce 
which  to  Dollar.'?,  take  the  followinjr 

RULE. 

Multiply  the  pouurit^  by  8 ;  d^^^diug  that  product  ])y  3,  i 
I  ,'^lvoa  the  doJlftTK;  and  where  there  arc  shillings  add" one  | 

i  '■Joll-ir  for  tvt^vv  "ir.  i^yj.  \ 

I 

i 


l?e.l 

uce  80/. 
30 

3j2l0 

1/v. 

to  dollars 

and 

C€nt8 

15 

80 

AnsTPer  ^82 

168  REDUCTION  OP  COINS. 

The  Dollar  passes  for  8  shillings  in  the  States  of  New 
York  and  North  Carolina.;  to  reduce  which  to  Dollars, 
ufae  this 

RULE, 

Multiply  the  pounds  by  2  J,  and  the  product  will  be  dol- 
lars; and  where  there  are  shillings,  add  one  dollar  for 
every  Ss, 

EXAMPLES. 

Reduce  30?.  12s.  to  dollars  and  cent^. 
30  12s. 

H 

60 
15 
12s.  =  1.50 

Answer  $76.50 

In  ttee  States  of  South  Carolina  and  Georgia^  the  Dollar 
passes  for  45.  and  Sd.  to  reduce  which  into  Dc  liars,  take 

RULE, 


■ 


Add  a  cypher  io  the  right  hand  of  the  pounds,  then  multi^ 
plv  by  5,  and  divide  by  7,  and  the  quotient  is  the  dollars ; 
and  it  mere  are  shillings,  add  a  dollar  for  evwy  4$.  8d. 

EXAMPLES. 

Reduce  10Z.  lOs.  to  dollars  and  cente 
100 
3 

7)300 

42.85.C 
9.<f.  4d.  -  2. 
8f  .14.2 

Answer  $45.00.0 


ramiXMammiimmmtf 


n  'i   '  ~il Ti' Ti '      ■  < «ii'in rii '  I ii«ir      1 1,  n  "'■Tliid  ' n ^ 


A  TABLE, 

Exhibiting  the  standard  weight,  and  Federal  value  of  the 
Gold  Coins,  that  pass  current  in  the  United  States,  with 
their  value  in  the  currencies  of  the  respective  States. 


-?^?  ?ri 


ts-*    P- 


P-   P-   S- 


a  «  a  5?  o 

^  5-  ^  ^    g 
.     p    .     .     . 


o 

CD 


o 

p- 


J3 


o 

p- 

p 
p 

CO 


8 


a. 

•I 


P5 


a-   ? 


CD 


•^ 

^ 


Co 


w 


o 

o 


to    O^    I-* 


^ 

s 


O    en    o    QftJ 


CO    Ot     CO    ><^     >i:^    O    GO    05 
-Jl-'OiCnOSOOO 

CnbOCOtOOiOOO 


ti  o«  o 

(yt  o  o 

o  o  o 

o  o  o 


fcOOOtO-^OOOSOOCi 
000050000 


O    M    CO     t^ 

Oi    o  •  O     J« 

O    O    O     fX 


Standard 
Weight. 


Federal 
Money. 


New  England 
States,  Virgi- 
nia, Kentucky 
and  Tennessee 


MC;iMMH-»b0     05<:75  H-ibOtf^t*< 


OOOOOOOO 


O    O    O     J» 
O    O    O     ft. 


New  York  and 
N,  Carolina. 


h^^>^}^i-itZ>ZOC^  OH-*COt*< 


OO    ti>    —  1     >+*    O^    C/«    O    O 
OOOOiOOOO 


00    -1    en     ?» 

O    O  "O     ft. 


New  Jersey, 
Pennsylvania, 
Delaware,  and 
Maryland. 


OCOOH*HJ|-»fcO>f^  0»-*b©t^ 


OOO^IM(-*COOO 
OOOSCJ^CDOOO 


H-*    CO    Ci     o» 
OO    t^    00     ft, 


South  Caroli- 
na &  Georgia. 


*The  Standard  for  Gold  Coins  of  the  United  States  is 
i  eleven  parts  fine,  to  one  part  aljoy;  Silver  Coins  1485  parts 
■  fine,  to  179  parts  alloy. 


^ ■x-ai>!,iini>ii«ftMii  I 


t  'tit^iNiaratf^tiMu:^ 


f  IVO 
f.-     / 


:|L' 


ri5 

< 


I  ABLE 


o 


so 

is* 


P  00   jcv^ 

^  *^  »^ 
5z;  (^"^  ic-i 


-^  Ir-I  IOC  ItT: 


O "--'  t'-^ 


Tj^    ICO 

^  Ice 

0^1     r-< 


iCO  jvN 
i»0  ■■'7~1 


o 


02  ^^ 


to 


(ji  o  cc  ICC' 

ICv5 


CO 


o  o 

CO 
CO 


CO   iO 

CO  |:.: 


IcO    (M  i'M 


CO 


<5  CI  H 


CC  jO-l 


|(M  'lr->i  J!— * 


V»%i— I  jo 
■^  OO  i«0 


■^1    Oi 


C3  r-< 


iC^ 


|X> 


jr^,   jo  |u-0 

!:->  Ico  i'O 

i    i    :co 


ir-l    vO   IO 

;cTj  r^  jco 
;     .."0  CO 


CO  -co 

JO    CO 


CO    o 

CO    CO 


M^   CO   CO 
CO    O    I--. 

CO    Ctt)  IcM 


jr^   pO    CO 

CO  c<i  ca 


>j^o  '^  r-"  o  >-o  1^  '"I'  fc»2  k^i  !c;4  !t=s 
.'S  CI  GO  rv£>  jco  ''-D  CO  o  jt--  h*  H  cr^ 
Ji; '"":.;  ic^^  CO  ico  '71  <:■?  ci  i— . 


'S  O  05 


,-1  \ta>  kd  1"^  M4  .:o 

CO  <r>  'co  lO  {^  kj< 
CO   CO  I^O  !g4  '^-nJ 


i^!c-i 


C  1  ifH    T— s    J— 1  j 


^  .-  ;^  »ro  l««*  h^  Ico  !co  \oi  irH 
.S  '-^  h^  «o  jco  iO  1I--  i-v?*  i^  Use 

.iC,         i         v^i  ^CO  iC«i  '?!  ■■•!    CI  P"^ 


J i 


b-  jcp  to  jo 


u^ 
c 


0  'O  Irti 


O 


iTt* 


"i  jO    ?^  !^  ''**'  I'X)  i'*i> 


jco    CO.  ICO   C^  i'^i  \Q^   r^ 


to  o  o  hf  hjf  (:o  Icri 

O    ?—   -"  I.— I  l.go    O  T'^^ 


!        I 


&4 

a 


uo  k^  O- 


<  ^  .-^  t-5  •-<  (©2 

I  .     i       (      -4  .....  !,      I 


tj    — 
-ft 


CO 


iTMir  iijr-  iB>»i 


Pi 


fcX) 

s 


a. 
o 

•♦J 


03 

S 

s 

a. 

<» 

DC 


CD 

> — 4 


^ 


O 

o 


I 


TABLE   OF  INTEREST, 

Pcj  day,  at  6  per  cent,  on  anj  number  of  Dollars,  from  One 
to  Twelve  Thousand. 


D. 

1 

2 

r, 
O 

4 
5 
6 
7 
8 
9 

10 
11 
12 
13 
14 
15 
10 
17 
18 
19 
20 
21 

oo 

23 
24 
25 
26 

27 


i.  2f 


M. 
I  016 
038 
049 
066 
082 
099 
115 
182 
148 
164 
I8i 
197 
214 
230 
247 
203 
279 
296 
312 
329 
345 
362 
37« 
395 
411 
427 
444 
^.60 
477 
498 


2! 

o 


D. 
31 

'32 
33- 
34 
35 
36 
37 
38 
39 
40 
41 
42 
48 
44 
45 
46 
47 
48 
49 
50 
51 
52 
153 
II  54 
55 
56 
57 
58 
59 
60 


M. 

510 
526 
542 

559 
575 

592 
608 
625 
641 

658 
674 
690 
707 
723  I 
740  , 
756  I 

<  i  O  ' 

789  i 

808  i 

822 

838 

855 

871 

888 

004 

021 
I  937 
'  053 
I  970 
:  986 


^" 


D. 

61 

62 

64 
65 

66 
67 

68 
69 
70 
71 

72 

73  I 

74  j 

75  ! 

/O  . 

«/  I 
78  j 
79 
80  ' 
81 
82  I 
83 
84 
85 

,  8^ 

l!  C^ 

fssj 

89 
\  90 


C. 

1, 

1 

1, 

I. 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

1 

I.  • 

1. 
1. 
1. 
1. 
1. 
1. 
1. 
1. 


M. 

003 
019 

036 

052 

068 

085 

101 

118 

134 

151 

167 

184 

200 

216 

233 

249 

266 

282 

299 

315 

332  11 

348 

364  !• 

381  jl 

397  |! 

414  I! 

447  '1 

468  I 
479  I 


5^ 


•^• 


D. 

91 

92 

93 

94 

95 

96 

97 

98 

99 

100 

200 

300  ^ 

400 

500 

600  j 

700  I 

800  I 

900  ' 

1000 

2000 

3000 

4000 

5000 

6000 

7000 

8000 

9000 

10000 

11000 

12000 


•oannM^UMa 


D.  C. 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

1. 

3. 

4. 

6. 

8. 

9. 
11. 
18. 
14. 
16. 
32. 
49. 
65. 
82. 
98. 
16. 
31. 
47. 
64. 
80. 
97. 


M. 

496 

512 

529 

545 

662 

678 

695 

611 

627 

644 

288 

932 

575 

219 

863 

507 

151 

795 

438  1 

877 

815 

763 

192 

630 

058 

507 

045 

884 

822 

260 


A  PRACTICAL  SYSTEM 


©F 


BOO  K-K  E  E  P  I  N  G, 

FOR 

FARMERS  AND  MECHANICS. 


Almost  all  persons,  in  thS  ordinary  avocations  of  life,  unless 
they  adopt  some  method  of  keeping  their  accounts  in  a  regular 
manner,  will  be  subjected  to  continual  losses  and  inconveniences ; 
to  prevent  wliich  the  following-  plan  or  outline  is  coiifposed, 
embracing  the  principles  of  Book-Keeping  in  the  most  simple 
form.  Before  the  pupil  commences  this  study,  it  will  not  be 
necessary  for  him  to  iiave  attended  to  all  the  rules  in  the  Arith- 
metic; but  he  should  make  himself  acquainted  with  the  subject 
of  Book-Keeping,  before  he  is  suffered  to  leave  school.  A  few 
examples  only  are  given,  barely  sufficient  to  give  the  learner  a 
view  of  the  manner  of  keeping  books;  it  being  intended  that 
the  pupil  should  be  required  to  compose  similar  ones,  and  in- 
sert them  in  a  book  adapted  to  tiiis  purpose. 

Book-Keeping  is  the  metiiod  of  recording  business  transac- 
tions. It  is  of  two  kinds  —  single  and  double  entry;  but  we 
shall  only  notice  the  former. 

Single  entry  is  the  simplest  foym  of  Book-Keeping,  and  is 
employed  by  retailers,  mechanics,  farmers^  &c.  It  requires  a 
Day-Book,  Leger,  and,  where  money  is  frequently  received  and 
paid  out,  a  Cash-Book. 


DAY-BOOK. 

This  book  should  be  a  minute  history  of  business  transac- 
tions in  the  order  of  time  in  which  they  occur;  it  should  be 
ruled  with  head  lines,  witli  one  column  on  the  leil  hand  for 
post-marks  and  references,  and  (wo  columns  on  the  right  for 
dollars  and  cents.  The  owner's  name,  the  town  or  city,  ^nd 
the  date  of  the  first  transaction,  should  stand  at  the  head  of  the 
first  page.  It  is  the  cuat<»n  of  tnany  to  continue  inserting  the 
name  of  the  town  on  every  page.  This,  lirnvever,  is  unneces- 
sary. It  is  sufficient  to  write  only  the  month,  day,  and  year, 
I  at  the  head  of  eacii  page  after  Llie  first.  This  should  be  writ- 
ten in  a  larger  hand  than  the  entries. 


(L7^4 


FORM   OF   A  DAT-BOOK. 


iO 


On  commencing  an  account  with  any  individual,  his  place 
of  residence  sliould  be  notod,  provided  it  is  not  l\v?,  same  as  that 
\vh(;re  the  hook  is  kept.  If  it  be  the  same,  this  is  unnecessary. 
As  it  often  happens  that  dillerent  persons  bear  tiie  same  nan^e, 
it  is  well,  in  such  castas,  to  (Jesitrnate  the  individual  with  whom 
the  account  is  opened,  by  L^fating  his  occupation,  or  particular 
place  of  residence. 

When  the  conditions  of  sale  or  purchase  vary  from  the  ordi- 
nary custo«is  of  the  place,  it  should  be  stated.  Every  month, 
or  oftener,  the  Day-I^ook  should  be  copied  or  posted  into  the 
Legcr,  as  hereaftjer  directed.  The  crasses,  on  the  left  hand 
column,  show  that  the  charge  or  credit,  against  which  they 
stand,  19  posted,  and  the  tigures  show  the  page  of  the  Leger 
whore  the  account  is^pposted.  Some  use  the  figures  only  as 
post-marks. 

Every  article  f=old  on  credit,  except  when  a  note  is  taken, 
should  be  iiiunediatcly  charged,  aa  it  is  always  unsafe  to  trust 
to  memory.  Also,  all  bbour  performed,  or  any  transaction 
whereby  another  is  made  indebted  to  us,  should  be  immediate- 
ly entered  on  the  Day-Book.  If  farmers  and  naechanics  would 
strictly  observe  this  rule,  they  would  not  only  save  many  quar- 
rels, but  much  money.  In  this  respect,  at  least,  follow  the 
example  of  Dr.  Franklin,  who  never  omitted  to  make  a  charge 
as  soon  as  it  could  be  done.  Never  defer  a  charge  till  to-mor- 
row, when  it  can  be  made  to-day>. 


Edward  L.  Peckham. 


•  Jan.  1,  1840. 


+ 
2  + 


James  Murray,  Jr Dr. 

To  Igall.  Lisbon  wine $1,92 

"  {)  yds.  C'Jlico,  a  '.M^  els <.- -     '2.^5 

"  2}Ms.  Broadcloth,  aS4,50 y,00 


Robert  Hawkins,  Blacksmith Dr. 


To  217  Ibg.  Iron,  a  8  cts. 


:^4- 


Thomas  Yoeman  . . .  • Cr. 

By  Casli 

.3 : 


Archihdd  Tracy.  Salem Dr. 

To  Oiie  jwece  Droadololh,  containing  2D  yds.,  a  $3  per  yd., 
S!0  days'  credit 


Jwacs  Warren^  Wartland Dr. 

To  J  cask  A'ojIs,  2-2j  lbs.,  a  8  cts 

Cr. 

By  :i7  lbs  Cheese,  a  10  cts $3.70 

"  41  \h^.  Fcalhors,  a  70  cte ■  28.70 

IJalance  to  be  paid  in  Corn,  at  market  price. 


18 


17 

3G 

75 

00 
00 


32   40 


^5-"^ 


J    II. -M  \v  .    ■!- 


2  + 
2-h 


rORM    OF   A    DAY-BOOK. 


Isaac  Ikomas^  Brattle  Square 
To  32  palls.  Molasses,  a  50  els 


J)r. 


William  AngelL 

7'a  300  IbP.  Porh,  at  7  ots. 
'■•   30  bu.  C<MH,  o  45  CIS.  . 


Dr. 

$•21,00  I 
13,50 


10 


C 
00 


■  H    3-}!  50 


Samioel  Stone Dt. 


I'o  50  lb.s  H.irncsa  Leather,  «  20  cts. 
••   7  Tons  Hsy,  «  810 


$15,00  \        , 
70.00  i         I 


George  Corpenier 

To  17  Brooms,  t  1:3  ctg 

"   7  lbs.  Butter,  a  20  cts 

"  4  lbs.  Cheese,  a  10  cts 


35,  00 


3-f 


3  + 


1  + 


Jesse  B.  Swuei.      ■'' 

To  1  hM.  Molaese?,  &8-^  ^  H2  /rails.,  a  30  cts. 


Dr.    \      I 

.     1.40  i'         I 
■       ,40  |! 


Dr. 


]■     27i  60 


Or. 


By  C.Hsh 


Jesse  Metcalj] 

To  20Ca!f-S.kiiis,  a$.^.. 
•'  59  Dried  Hides,  a  ^. 

60  days'  credit. 


Dr. 

$100,00 
200,00 


James  Murray y  Jr Cr. 


By  20  !>u.  CJorn,  a  CO  cts. 
"  4  bu.  Oats,  a  40  cts.  . 


$13,00 
l,«iO 


*    James  Warren  . . 
!  To  24  bu.  Corn,  a  CO  cts. 


Dr. 


Archibald  Tracii, Dr. 


To  1  cord  Wc/d   

"  30  lbs.  Feathers,  a  70  cts. 


$6,00 
21,00 


1  + 


Robert  Haivlcins Cr. 


By  shoeinu  my  HT)rs>e. 
"        "  "    Oxen  . 


$2.00 
3,00 


— i 


Samuel  Stone Dr. 


To  2  yds.  Broadcloth,  a  $4 
"   4  pr.  Shoes,  a  $1 


$8,00 
4.00 


15 

1 
00 

300 

i    - 
i 

00 

1 
t 

1    '' 

CO 

14 

1 
i 

4t) 

27 

00 

5 

t 

.00 

! 
!     12 

00 

FORM    OF    A    I>AY-BOOK. 

Jaji  5,  1840. 


17  o' 


2-f 


Thomas  Yeomans Dr. 


To  200  bu.  Corn,  a  70  cts. 


?!        C 

110  yo 


To  30  quiiitaM  Fiab,  a  $3,75 


>  ^  i       Archibald  Tracy Br. 

i  To'^bbls.  Flour,  agllO $20,00  j 

.  I  ••  25  bb!5.  Lard,  «  10  cts 2,50  | 

I  "  3I)U.  Satt.at^U.-t? lr'8  ! 


I)r. 


•^-1,         Gcorgr.  Carpenter Dr. 

ToQOO  lbs.  t'hc^sc,  a  r  cia $10,00 

••  1  flrkin  Butlo.r,  7H  lbs.,  weitfhl  of  lub,  10  lb9.»66, 

a  SI)  cts.    •    13.20 


112 


SO 


ea  » 


!     2i 


^-f 


Isaac  Thomas Dr. 

To  50  yds.  Cnlico,  n  "Tl  cts .'$11,00 

"  75  yda.  brown  Shcotiiii;,  a  J 1  't-< 10,50  |i 


Cr. 


By  Order  on  Goodrich  St  Lnrd.  for  ^U. 


12 


3H 

2  + 


Jesse  Melcalf Dr. 

To  500  pr.  Men's  Bhoos,  a  95  cts \\  475 

. 10 

Thomas  Yeomans  . , Di\ 

Po3  bbls.  Flour,  c  !;^,50 %^ 


Robert  Hawkins  .'. Dr.     j 

'^o  ViO  ib'J.  bii3tered  Stetil,  a  ij  cls S^.CO  j 

*'  W)  lbs.  ltu.ssi,-.  Iron,  a  5  cts 5,00  jj 


28 


14 


James  Murray,  Jr Dr,    \\ 

To  10  lbs.  Suj!Hr,  a  11  cts 81. 10  ll 

"  iG  lbs.  Cotiee,  a  15  cl.s. 3,00  jj 

"  6  gallB.  Molasses,  o  37  cts •    2.^2 


WUliam  Angdl Cr. 

ny  200  lbs.  L.ird,  a  (j  eta $12,00 

"  :},50  Iba.  Ilacon,  a  V.  cts 42,00 


18 

50 
80 

oc» 

50 


60 


32 


541  00 


^1'76 


LEGER. 

Jan.  9,  1840. 


3  + 


+ 


James  Hammond Dr. 

To  1  bbl.  Flour $10,00 

"  3  bu.  Corn,  a  65  cts 1.95 

"  f.  palls.  Wine,  a  1,25 7,50 

"  3  lbs.  Coffee,  ff  1(>  els .■ 48 

"  4  bu.  Salt,  a  70  cts 2,80 

"  1  Jb.  Y.  H.  Tea 1,25 

"  14  lbs  Sugar,  a  12  cts 1,68 

"  3  vds.  Broadclotli,  a  $,2,')0 7,50 

"  12  yds.  Shirting,  a  19  cts 2,28 

13 

Jame^  Murray^  Jr Dr. 

ToG  lbs.  Raisins,  n  20  cts. .* $1,20 

"  5  galls.  Currant  Wine,  «  75  cts 3,75 


35 


44 


95 


LEGER. 

This  book  is  used  to  collect  the  scattered  accountB  of  the  Day- 
Book,  and  to  arrange  all  that  relates  to  each  individual  into  one 
separate  statement.  The  business  of  collecting  these  accounts 
from  the  Day-Book,  and  writing*  them  in  the^Leger,  is  called 
posting.  This  should  be  done  once  a  month,  or  oftener.  Debts 
due  from  others,  and  entered  upon  the  Day-Book,  are  placed  on 
the  side  of  Dr. ;  whatever  is  on  the  Day-book  as  due  to  another 
is  placed  on  the  side  of  Or. 

When  an  account  is  posted,*  the  page  of  the  Legor,  in  which 
this  account  i.s  kept,  is  xvritten  in  the  left  hand  column  of  the 
Day-Book. 

Every  Leger  should  have  an  alphabetical  Index,  where  the 
names  of  the  several  persons,  whose  accounts  are  kept  in  the 
Leger,  should  be  written,  and  the  page  noted  down. 

When  one  Leger  is  full,  and  a  new  one  is  opened,  the  accounts 
in  the  former  should  be  all  balanced,  and  the  balances  transferred 
to  the  new  Leger. 


EXPLANATION  OF  THE  LEGEE,  AND  THE 
MANNEil  OF  POSTING. 

It  will  be  seen  that  the  name  of  James  Murray,  Jr.,  stands 
first  on  the  Day-Book;  of  course,  we  shall  post  his  account 
first.  We  enter  his  nanie  on  the  first  page  of  the  Leger,  in 
a  large,  fair  hand,  writing  Dr.  on  the  left,  and  Cr.  on  the  right. 
At  the  top  of  the  left  hand  column,  we  enter  the  year,  under 
which  we  write  the  month  and  day  when  the  first  charge  was 
made  in  the  Day-Book,  and  in  the  next  column  the  page  of  tjse 


f- 


FOPvM    OF   A    r.KOER. 


177 


Day  Book  where  the  charge  stands. 
apti':le3  ia  the  first  chrirg-e,  instead 


Then,  as  there  are  several 

of  specifying  each  article, 

J  as  in  the  Day-Book,  we  merely  say,   To  Sundries,  and  enter 

]  the  amonnt  in  the  proper  columns.     This  charge  being  thus 

i  posted,  we  write  the  page  of  the  Leger,  viz.,  1,  in  the  left  hand 

■column   of  the  Day-Book,  and    opposite    to   it  a  -f,  to   show' 

i  more   distinctly  that   the   charge  is  posted.     We  then   pass  a 

finger  carefully  over  the  names,  till  we  again  come  to  the  name 

\  of  James  Murray,  Jr.,  which  we  find  on  the  second  page;  but, 

las  this  is  credit,  we  enter  it  on  the  credit  side,  with  the  date 

I  and  page  in  their  proper  columns.     We  then  enter  the  Loger- 

;  page  and  cross,  as  before,  and  then  proceed  again  in  search  of 

!  the  same  name,  until   every  charge   and  credit  is  transferred 

;  into  the  Leger.     The  next  name  is  to  be  taken  and  proceeded 

with  in  the  same  way  as  the  first;  and  so  continue  till  all  the 

accounts  are  posted. 

As  it  is  uncertain  how  extensive  an  account  may  be  when 
once  opened,  it  is  better  to  take  a  new  page  for  every  name, 
until  all  the  Leger  pages  are  occupied.  By  this  time,  it  is  pro- 
bable, several  accounts  will  have  been  settled,  we  may  then 
enter  a  second  name  on  the  same  page,  and  so  continue  till  all 
the  pages  are  full. 

Whenever  any  account  is  settled,  the  amount  or  the  Iwlance 
is  ascertained,  and  the  settlement  entered  in  the  Leger.  The 
settlement  may  also  be  entered  in  tiie  Day-Book;  and  many 
practice  this,  although  it  is  not  essentially  necessary.  But  it 
ia  es.senlially  necessary  that  one,  if  not  both  the  books,  should 
show  how  every  account  is  settled,  whether  by  cash,  note, 
order,  goods,  or  whatever  way  tiie  amount  or  balance  m  liqui- 
dated. 

N.  B.  In  making  out  bills,  the  Leger  is  used  as  a  reference  to 
the  charges  in  the  Day-Book,  which  must  be  exactly  copied. 

FORxM  OF  A  LEGER. 


D 


r. 


James  Murray^  Jr. 


Cr. 


Jan.  1. 
"  10. 
"     13. 


To  Sundries, 
do. 
do. 


13 
0 
4 

951 

1829. 

Jan.  5. 

"    15. 

2 

$•21 

4-1 

By  Corn  and  Oats, 
By  Cash,  to  bal., 


«24 


D 


r. 


Robert  Hawkins, 


Cr. 


18ii9. 
Jan.    1. 
"     10. 


To  Iron, 

"  Sundries, 


c  I      1829. 


17361 
14  GO, 

$31  UGl 


Jan     6. 
"      12. 


By  Work, 

"  Note,  aGOdays, 


2G 


$31  96 


[iii 


rirf  Till     iiiiMinini  II    -       — -dirr- 


rOIlM   OF  A   LEGER. 


Oi 


L^l 


Dr. 


Thomas  Yeomans. 


Cr.  . 


Jan.    7. 
••      10. 


To  Corn, 
".  Flour, 


$     \c 
14000 

2850' 

« 168  50 


18^9. 

Jan.    1. 

"      11. 


By  Cash, 
"  Check  for  bal 


$      c 

75175 

.  9*  75 

S1C850 


Br. 


Archibald  Tracy, 


Cr. 


1829. 
Jan.    3. 
«       6. 
9. 


To  Broadcloth, 
"  Sundries, 

do. 


a 

(• 

18^. 

87 

00 

Apr.    2. 

'i7 

00 

24 

"IF 

$138 

48 

By  Cash. 


138 


D) 


James  Warren. 


Cr. 


■   1829. 
Jan.    3. 
6. 


To  NaiJs, 
Corn, 


1800 
1440 


$32|40 


:    ifej9. 
Jan.    3. 


By  S^indrieB, 


32 


40 


Dr. 


Isaac  Thomas. 


Cr. 


1829. 

Jan.    n. 

".      9. 


To  Molasses, 
"  Sumlrios, 


50 


1829. 

Jan.    9. 

"      20. 


By  Order, 
"  Note,  a  90  days, 


12180 

2470 

|37l.^i 


Dr. 


Willmm  An  sell. 


Cr. 


1829. 

Jan.    4. 

"      1(5. 


To  SiindrieR, 
"  Cash, 


34 

19 

I    $54 


c  1|     1829. 
50  Uan.  10. 
50  1 


00 


.'>4!00 


Dr. 


Samml  Stone. 


Cr. 


1829 
Jan.    *. 


To  Sundries. 
do. 


1S2^">. 
85'00|lJan.  30. 


00 


By  CaeU, 


97  00 


Dr. 


George  Carpenter. 


Cr. 


182'. 
Jan.    5. 
9. 


To  Sundries, 
do. 


$    i  e  I) 

3,84 
29  20 

833:04 1 


1829. 
Jan.  15. 


I    $    i  r 
Ov  note,  a  30  daye       33  04 


■MM«tHk«aaiMMCiaHm>N0M 


CariX;nt''J'  Grcoigti 2 

i                     T 

Thomas,  Isaac   2 

H 

Tracy,  Archibald 2 

Hawkins,  Ilobcrt , , .  ] 

IlaiTiuioiid,  James  • .  • 3 

W 

M 

Murray,  James 1 

y 

Yeomann,  Thomas 3 

Mctcalf,  JcBSO  • 3 

CASH-BOOK. 

Thif  book  records  the  p^ymeiUG  ttuJ  receipts  of  casft. 

It  18  kept  by  maki'^ff  cash  Dt.  lo  catJi  oi;  hand  and  what  in  rscei  vied,  and  Or. 
by  whatever  ia  paid  cut. 

!     At  the  end  of  every  day  or  v/aok,  aa  may  beat  suit  the  nati;fc  of  tha  bjBinese, 
the  cash  on  hand  is  c cuntod,  ,~nd  entered  on  th«  O.  side. 

If  there  is  no  on-cr,  luu  wii!  maku  th<i  bum  of  the  Dr.  equal  to  t!iat  of  the 
Cr.  A  bclancc  i*  t.ion  tftruok,  iir,<l  the  c^aii  on  Land  curriMl  a^ain  xi^n  tao  Ih. 
side. 


»'»-'«r<u'i  "rTir     nri 


TX^ 


4     BILLS. 

FOEM.OF  A  CASH  BOOK. 
CASH. 


Cr. 


To  Cash  on  hand 

"  J.  Thompson 

"  Hart,  paid  acc't. 

"  H  Palmer  on  note 

*'  S.  Snowdou 

"  f.  Mcrvin  on  acc't. 

*'  8.  Crane 
Sixies  of  Merchandise 


Casii  on  hand, 


637150 
37194 

651-13 

m\2S 

84,73 

1790 

100  'JO 

311  18 


1382 


550 


86 


(55 


I  1827. 
Jan.  2 


By  rent  of  store  for 
one   quarter,   paid 
Thomas  Taylor, 
"  Paid    note    to    R. 

Thacher, 
"  Family  expenses, 
"  Merchandise     bo't 

of  T.  Thamor, 
Cash  on  hana, 


62 

127 

27 

614 

550 


1382 


Form  of  a  Bill  from  the  preceding  Work. 

Mr.  Jambs  Murray 

To  Edward  L.  Peckham,    Dr. 


1629. 

'an.  1.    To  1  gall   Li;;l'f>n  VVm-: 

"    6  vds.  Calico,  a  37J-  els.    .  . 
'      "      "    2  yds.  Broadcloth,  a  §4.50. 


2  26 
9^00 


10    To  10  lbs.  Sugar,  a  11  cts i  ,10 

"      "    6  flails.  Molasses,  c  37i  ct3 "2,22 

"      "    20  Ibd.  Coffee,  a  15  cts 3,00 


12    '■  .C  Ibg.  Raisins,  a  20  ctB 1,20 

"     "    5  galls.  Currant  Wine,  a  75  cts 3,75 

Cr. 

5  By  20  bu.  Corn,  a  60  cti = . . .  = 12,00 

"    "  4  bu.  Oats,  a  40  cty ]  ,00 

15  "  Cash  to  balance 10,04 

Errors  o.vcpputil,  

KinVVARii  I.   PECKHAM. 
Juniutry  1/";.  h.m 


13 


17 

32 

95  ! 

I 

44 

44^ 


2d  Form. 
Mr.  Jesse  Metcalf 

To  E.  L.  Peck  HAM, 

1829. 

ian.  5.    To  20  Calt-SkiBs,  a  $5 

••      "      •'   50,  Dried  Hides,  a  $4 * 

""     •'      "   500  pr.  Men's  Shoes,  a  95  eta 


JDr. 


Received  payment,  by  his  check,  on  N.  E.  Bank.  3S775 

^pril  7,  IdiJ.  EDWARD  L.  PECKHAM 


9    c 


100 
200 
475 


j  Ao.  1.  Mgotiabk  JVwi 

?i^-  --^-   *Wai^  25,  1827. 

Oo,„  a^""  ^'""-^  w'-^  ?r'^^.*^  £*^  ^^^^^«  Lorraine,  or 
jO.'uor,  Seyenty^ight  BoUai^  Fifty  6ent8,  with  Interest,  for 
JTalue  received,  ' 

JAMES  HONKSTUS. 


Ab.  2,  Aote  payable  to  Bearer. 


Sept.  17,  1827. 


Six  months  from  date,  I  promise  to  pay  A.  B.. 
lie&rer,  Forty  Dolkra  for  value  received. 


or 


SIMEON  PAYWELL.     . 


•^<?«  3,  ^o^g  5j^  fjffQ  Persons. 


!5^'  --         Oc^  28,  1827. 

,  For  value  received,  we,  jointly  and  severally,  pro- 

mise  to  pay  C.  D,  or  Order,  on  demand,  Five  Hundred 
Dollars,  with  Interest. 

HORACE  WALCOTT. 
JAMES  HART. 


^0'  4.  JSpoU  at  Bank. 


!1^  -         Fed.  25,  1819. 


Ninety-fivo  days  from  date,  I  promise  to  pay  Tbo- 
m^  Andrews  or  Order,  at  the  Phoenix  Bank,  One  Huu,imi 
and  i^lfty  Dollarfl,  for  value  received. 

JOHN  REYNOJ..W 


wj'^^aian  I 


'     '  "i"     ■■^^f|V 


;    iirmiuM »  |-p-..,-. ^,  -Mi-iar  ■iiifirtMnri<>.iiirwii<rr»j--»«wr«»>iitin»i«ir»»wraaMa«iagiM<<aiMa»»M^^ 

182  MERCANTILE   FORMS; 


Remarks  relating  to  JSfotes  of  Hand, 

1.  A  negotiable  note  is  one  which  is  made  payable  to  A.  B. 
or  order. — It  ie  otherwise,  when  these  words  are  omitted. 

2.  By  endorsing  a  note  is  understood,  that  the  person  to  wlwra 
it  is  payable  writes  his  name  on  the  back  of  it.     For  additional  1 
soojrity,  any  other  person  may  afterwards  endorse  it 

3.  If  the  note  be  made  payable  to  A.  B.,  or  order,  {see  No.  1,) 
th'cn  A.  B.  can  sell  said  note  to  whom  he  pleases,  provided  he 
endorsee  it ;  and  whoever  buys  said  note  may  lawfully  demand 
payment  of  the  signer  of  the  note,  and  if  the  signer,  through 
inability  or  otherwise,  refuses  to  pay  said  note,  the  purchaser 
may  lawfully  demand  payment  of  the  endorser. 

4.  If  the  note  be  made  payable  to  A.  B.,  or  bearer^  (see  No. 
2,)  then  the  signer  only  is  responsible  to  any  one  who  may 
purchase  it.  -j 

6.  Unless  a  note  be  written  payable  on  some  specific  future  i 
time,  it  should  be  written  on  demand;  but  should  the  words! 
on  demand  be  omitted,  the  note  ie  suppo.sed  to  be  recoverable  i 
\Tj  law.  I 

6.  When  a  note,  payable  at  a  future  day,  becomes  due,  it  is  ■ 
XfiiE'.dered  on  hilercst  from  that  time  till  payed,  though  no  men-  j 
\ion  be  made  of  interest. 

7.  No  mention  r.oed  be  made  in  a  note  of  the  rate  of  interest : 
that  particular  is  s^jftled  by  lav^,  and  may  be  collected  according  to 
the  laws  of  the  f/ate  where  the  note  is  dated.    In  some  states! 
it  is  6  per  cent, ;  in  others,  7. 

8.  If  twc  p€'ff<-ns,  jointly  and  severally,  {see  No.  3,)  sign  a 
note,  it  may  iK;  collected  by  law  of  either. 

9.  A  nAe  if.  liot  valid,  unless  the  words  for  value  received  be 
expressed. 

10.  "When  a  note  is  given,  payable  in  any  article  of  mer- 
jchandise,  or  property  other  than  money,  deliverable  on  a  speci- 
fied time,  such  articles  should  be  rendered  in  payment  at  said  [ 

jtirae,  othefvvise  the  holder  of  the  note  may  demand  the  value  in 
'money. 


MERCANTILE   FOBMS.  18^^ 

Account  unih  Interest 

Mr.  Thomas  I.  Spencer 

To  H.  Tlsd.ill,  Dr, 

l816-~Nor.  1.  To  3  yards  Cloth,  a  §7,50  per  yd. .  $22,50 

IQIO     ?^-  ?•"    ^i^'-^J^^-  Wine,  a    4,25  per  gall.  25,50 

1810— Jan.   1.  ''    Balance  of  Interest  ..... .    .  5,80 

^53^ 

'  I 

Supra,  Cr. 

1817— Nov.  1.     Bv  Cnsh $226ol 

1819— Jan.  1.     Ihtto  in  full *.'*     31^301 

^^3^1 
v.-      Jan.  1,  1819.  H.  TI«DALL. 


Receipt  for  Money  on  Account.  j 

Re^p.iYed  of  Jamea  Wardell,  Three  Dollars  on  account 

SIMEON  BB.ANJ>T. 
w.  -     /wne21,  1816. 


^  --     Dec.  31,  1827. 


A  General  Receipt. 

nOR.VCE  EITTKB 


Rec^^ived  of  Jonathan  Andrewfl,  Fonrt<Mia  I^nara  Jo 

fuU  of  all  account*. 


Receipt  for  Money  paid  on  a  JSoie, 

Received  of  L(=^onard  Teraple,  Seventy-two  Pounds  and 
Eleven  Shillings,  on  hi^  noto  for  t]j3  m\m  of  One  Hundred 
and  Sc-Tonty-two  PoimAs,  and  diitcd  at  Enfield,  Oct  27, 1826. 

D.THOMAS.     ,, 

}^  Boston,  August  27,  1828.  ij 

«-.rK^       .»  iiauw  MiHI,i^lWa—^BWl^HaSWBCfal-JMU        .  I ..  IM    11  Mini    '    ■!..  HI  .!■   .11   1 1   ■  i  ^F— ** 


HEECANTILE  FORMS,  1 


An  Order  for  Mone^c 

BIesses.  E,  PottES  &  Co. 

Pay  Jamc.^s  Tliotiias,  c?  Ote,  ^8t«ii  iss^^liere^  iSkd 
this  shall  be  yoiir  receipt  for  the  samOo 

SHEELAH  SPBNCEE. 
BepL  %  1828. 


o^n  Order  for  GcoiSo 

Mr.  -Alexon  N.  Olney, 

Pay  the  Bearer  Scventy-one  Dollars^  m  Goods  from ; 
■jyour  store^  and  charge 

Your  obedient  Rervant, 

Oxford,  Dec.  31,  1827.  R.  RAYNALL. 


«»  A  receipt  gketi  in  full  of  &U  accounts  cuts  off 
aoeounta  only ;  but  a  receipt  given  in  full  of  all  demands 
0iste  off  not  Guly  all  accounts,  but  all  demands  whatever. 

An  order,  when-  paid,  should  be  receipted  on  the  back,  by 
the  person  to  whom  it  is  made  payable,  or  by  some  one  duly 
siithorised  to  sign  for  him ;  but  when  it  is  made  payable  to 
be&refj  or  to  A.  B.  or  hearer^  it  may  b^  received  by  any  one 
who  preeeate  it  for  pajmeci 


7BS    IHJD. 


>''TqTr.,'.«V'..:>:T'gr^.*y.'»X.Strf.j:*t^-iJ3MJ^ 


